Arithmetic and Geometry : : Ten Years in Alpbach (AMS-202) / / ed. by Gisbert Wüstholz, Clemens Fuchs.
Arithmetic and Geometry presents highlights of recent work in arithmetic algebraic geometry by some of the world's leading mathematicians. Together, these 2016 lectures-which were delivered in celebration of the tenth anniversary of the annual summer workshops in Alpbach, Austria-provide an int...
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Arithmetic and Geometry : Ten Years in Alpbach (AMS-202) / ed. by Gisbert Wüstholz, Clemens Fuchs. Princeton, NJ : Princeton University Press, [2019] ©2019 1 online resource (186 p.) : 1 b/w illus. text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Annals of Mathematics Studies ; 202 Frontmatter -- Contents -- Preface -- 1. Introduction -- 2. Local Shimura Varieties: Minicourse Given by Peter Scholze -- 3. Hyperelliptic Continued Fractions and Generalized Jacobians: Minicourse Given by Umberto Zannier -- 4. Faltings Heights and L-functions: Minicourse Given by Shou-Wu Zhang -- List of Contributors restricted access http://purl.org/coar/access_right/c_16ec online access with authorization star Arithmetic and Geometry presents highlights of recent work in arithmetic algebraic geometry by some of the world's leading mathematicians. Together, these 2016 lectures-which were delivered in celebration of the tenth anniversary of the annual summer workshops in Alpbach, Austria-provide an introduction to high-level research on three topics: Shimura varieties, hyperelliptic continued fractions and generalized Jacobians, and Faltings height and L-functions. The book consists of notes, written by young researchers, on three sets of lectures or minicourses given at Alpbach.The first course, taught by Peter Scholze, contains his recent results dealing with the local Langlands conjecture. The fundamental question is whether for a given datum there exists a so-called local Shimura variety. In some cases, they exist in the category of rigid analytic spaces; in others, one has to use Scholze's perfectoid spaces.The second course, taught by Umberto Zannier, addresses the famous Pell equation-not in the classical setting but rather with the so-called polynomial Pell equation, where the integers are replaced by polynomials in one variable with complex coefficients, which leads to the study of hyperelliptic continued fractions and generalized Jacobians.The third course, taught by Shou-Wu Zhang, originates in the Chowla-Selberg formula, which was taken up by Gross and Zagier to relate values of the L-function for elliptic curves with the height of Heegner points on the curves. Zhang, X. Yuan, and Wei Zhang prove the Gross-Zagier formula on Shimura curves and verify the Colmez conjecture on average. Issued also in print. Mode of access: Internet via World Wide Web. In English. Description based on online resource; title from PDF title page (publisher's Web site, viewed 31. Jan 2022) Arithmetical algebraic geometry. MATHEMATICS / Arithmetic. bisacsh Abelian variety. Algebraic geometry. Algebraic independence. Algebraic space. Analytic number theory. Arbitrarily large. Automorphic form. Automorphism. Base change. Big O notation. Class number formula. Cohomology. Complex multiplication. Computation. Conjecture. Conjugacy class. Continued fraction. Cusp form. Diagram (category theory). Dimension. Diophantine equation. Diophantine geometry. Discriminant. Divisible group. Double coset. Eisenstein series. Endomorphism. Equation. Existential quantification. Exponential map (Riemannian geometry). Fiber bundle. Floor and ceiling functions. Formal group. Formal power series. Formal scheme. Fundamental group. Geometric Langlands correspondence. Geometry. Heegner point. Hodge structure. Hodge theory. Homomorphism. I0. Integer. Intersection number. Irreducible component. Isogeny. Isomorphism class. Jacobian variety. L-function. Langlands dual group. Laurent series. Linear combination. Local system. Logarithmic derivative. Logarithmic form. Mathematics. Modular form. Moduli space. Monotonic function. Natural topology. P-adic analysis. P-adic number. Pell's equation. Perverse sheaf. Polylogarithm. Polynomial. Power series. Presheaf (category theory). Prime number. Projective space. Quaternion algebra. Rational point. Real number. Reductive group. Rigid analytic space. Roth's theorem. Series expansion. Shafarevich conjecture. Sheaf (mathematics). Shimura variety. Siegel zero. Special case. Stack (mathematics). Subset. Summation. Szpiro's conjecture. Tate conjecture. Tate module. Taylor series. Theorem. Theta function. Topological ring. Topology. Torsor (algebraic geometry). Upper and lower bounds. Vector bundle. Weil group. Witt vector. Zariski topology. Capuano, Laura, contributor. ctb https://id.loc.gov/vocabulary/relators/ctb Fuchs, Clemens, editor. edt http://id.loc.gov/vocabulary/relators/edt Gao, Ziyang, contributor. ctb https://id.loc.gov/vocabulary/relators/ctb Gorchinskiy, Sergey, contributor. ctb https://id.loc.gov/vocabulary/relators/ctb Jossen, Peter, contributor. ctb https://id.loc.gov/vocabulary/relators/ctb Kanel, Rafael von, contributor. ctb https://id.loc.gov/vocabulary/relators/ctb Karolus, Christina, contributor. ctb https://id.loc.gov/vocabulary/relators/ctb Kuhne, Lars, contributor. ctb https://id.loc.gov/vocabulary/relators/ctb Mocz, Lucia, contributor. ctb https://id.loc.gov/vocabulary/relators/ctb Veneziano, Francesco, contributor. ctb https://id.loc.gov/vocabulary/relators/ctb Wustholz, Gisbert, contributor. ctb https://id.loc.gov/vocabulary/relators/ctb Wüstholz, Gisbert, editor. edt http://id.loc.gov/vocabulary/relators/edt Title is part of eBook package: De Gruyter EBOOK PACKAGE COMPLETE 2019 English 9783110610765 Title is part of eBook package: De Gruyter EBOOK PACKAGE COMPLETE 2019 9783110664232 ZDB-23-DGG Title is part of eBook package: De Gruyter EBOOK PACKAGE Mathematics 2019 English 9783110610406 Title is part of eBook package: De Gruyter EBOOK PACKAGE Mathematics 2019 9783110606362 ZDB-23-DMA Title is part of eBook package: De Gruyter Princeton Annals of Mathematics eBook-Package 1940-2020 9783110494914 ZDB-23-PMB Title is part of eBook package: De Gruyter Princeton University Press Complete eBook-Package 2019 9783110663365 print 9780691193786 https://doi.org/10.1515/9780691197548?locatt=mode:legacy https://www.degruyter.com/isbn/9780691197548 Cover https://www.degruyter.com/document/cover/isbn/9780691197548/original |
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Capuano, Laura, Capuano, Laura, Fuchs, Clemens, Fuchs, Clemens, Gao, Ziyang, Gao, Ziyang, Gorchinskiy, Sergey, Gorchinskiy, Sergey, Jossen, Peter, Jossen, Peter, Kanel, Rafael von, Kanel, Rafael von, Karolus, Christina, Karolus, Christina, Kuhne, Lars, Kuhne, Lars, Mocz, Lucia, Mocz, Lucia, Veneziano, Francesco, Veneziano, Francesco, Wustholz, Gisbert, Wustholz, Gisbert, Wüstholz, Gisbert, Wüstholz, Gisbert, |
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Capuano, Laura, Capuano, Laura, Fuchs, Clemens, Fuchs, Clemens, Gao, Ziyang, Gao, Ziyang, Gorchinskiy, Sergey, Gorchinskiy, Sergey, Jossen, Peter, Jossen, Peter, Kanel, Rafael von, Kanel, Rafael von, Karolus, Christina, Karolus, Christina, Kuhne, Lars, Kuhne, Lars, Mocz, Lucia, Mocz, Lucia, Veneziano, Francesco, Veneziano, Francesco, Wustholz, Gisbert, Wustholz, Gisbert, Wüstholz, Gisbert, Wüstholz, Gisbert, |
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MitwirkendeR MitwirkendeR HerausgeberIn HerausgeberIn MitwirkendeR MitwirkendeR MitwirkendeR MitwirkendeR MitwirkendeR MitwirkendeR MitwirkendeR MitwirkendeR MitwirkendeR MitwirkendeR MitwirkendeR MitwirkendeR MitwirkendeR MitwirkendeR MitwirkendeR MitwirkendeR MitwirkendeR MitwirkendeR HerausgeberIn HerausgeberIn |
author_sort |
Capuano, Laura, |
title |
Arithmetic and Geometry : Ten Years in Alpbach (AMS-202) / |
spellingShingle |
Arithmetic and Geometry : Ten Years in Alpbach (AMS-202) / Annals of Mathematics Studies ; Frontmatter -- Contents -- Preface -- 1. Introduction -- 2. Local Shimura Varieties: Minicourse Given by Peter Scholze -- 3. Hyperelliptic Continued Fractions and Generalized Jacobians: Minicourse Given by Umberto Zannier -- 4. Faltings Heights and L-functions: Minicourse Given by Shou-Wu Zhang -- List of Contributors |
title_sub |
Ten Years in Alpbach (AMS-202) / |
title_full |
Arithmetic and Geometry : Ten Years in Alpbach (AMS-202) / ed. by Gisbert Wüstholz, Clemens Fuchs. |
title_fullStr |
Arithmetic and Geometry : Ten Years in Alpbach (AMS-202) / ed. by Gisbert Wüstholz, Clemens Fuchs. |
title_full_unstemmed |
Arithmetic and Geometry : Ten Years in Alpbach (AMS-202) / ed. by Gisbert Wüstholz, Clemens Fuchs. |
title_auth |
Arithmetic and Geometry : Ten Years in Alpbach (AMS-202) / |
title_alt |
Frontmatter -- Contents -- Preface -- 1. Introduction -- 2. Local Shimura Varieties: Minicourse Given by Peter Scholze -- 3. Hyperelliptic Continued Fractions and Generalized Jacobians: Minicourse Given by Umberto Zannier -- 4. Faltings Heights and L-functions: Minicourse Given by Shou-Wu Zhang -- List of Contributors |
title_new |
Arithmetic and Geometry : |
title_sort |
arithmetic and geometry : ten years in alpbach (ams-202) / |
series |
Annals of Mathematics Studies ; |
series2 |
Annals of Mathematics Studies ; |
publisher |
Princeton University Press, |
publishDate |
2019 |
physical |
1 online resource (186 p.) : 1 b/w illus. Issued also in print. |
contents |
Frontmatter -- Contents -- Preface -- 1. Introduction -- 2. Local Shimura Varieties: Minicourse Given by Peter Scholze -- 3. Hyperelliptic Continued Fractions and Generalized Jacobians: Minicourse Given by Umberto Zannier -- 4. Faltings Heights and L-functions: Minicourse Given by Shou-Wu Zhang -- List of Contributors |
isbn |
9780691197548 9783110610765 9783110664232 9783110610406 9783110606362 9783110494914 9783110663365 9780691193786 |
callnumber-first |
Q - Science |
callnumber-subject |
QA - Mathematics |
callnumber-label |
QA242 |
callnumber-sort |
QA 3242.5 A7 42020 |
url |
https://doi.org/10.1515/9780691197548?locatt=mode:legacy https://www.degruyter.com/isbn/9780691197548 https://www.degruyter.com/document/cover/isbn/9780691197548/original |
illustrated |
Illustrated |
dewey-hundreds |
500 - Science |
dewey-tens |
510 - Mathematics |
dewey-ones |
516 - Geometry |
dewey-full |
516.35 |
dewey-sort |
3516.35 |
dewey-raw |
516.35 |
dewey-search |
516.35 |
doi_str_mv |
10.1515/9780691197548?locatt=mode:legacy |
oclc_num |
1125194243 |
work_keys_str_mv |
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n |
ids_txt_mv |
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Title is part of eBook package: De Gruyter EBOOK PACKAGE COMPLETE 2019 English Title is part of eBook package: De Gruyter EBOOK PACKAGE COMPLETE 2019 Title is part of eBook package: De Gruyter EBOOK PACKAGE Mathematics 2019 English Title is part of eBook package: De Gruyter EBOOK PACKAGE Mathematics 2019 Title is part of eBook package: De Gruyter Princeton Annals of Mathematics eBook-Package 1940-2020 Title is part of eBook package: De Gruyter Princeton University Press Complete eBook-Package 2019 |
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form.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Moduli space.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Monotonic function.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Natural topology.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">P-adic analysis.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">P-adic number.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Pell's equation.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Perverse sheaf.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Polylogarithm.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Polynomial.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Power series.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Presheaf (category theory).</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Prime number.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Projective space.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Quaternion algebra.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Rational point.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Real number.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Reductive group.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Rigid analytic space.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Roth's theorem.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Series expansion.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Shafarevich conjecture.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Sheaf (mathematics).</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Shimura variety.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Siegel zero.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Special case.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Stack (mathematics).</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Subset.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Summation.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Szpiro's conjecture.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Tate conjecture.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Tate module.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Taylor series.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Theorem.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Theta function.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Topological ring.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Topology.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Torsor (algebraic geometry).</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Upper and lower bounds.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Vector bundle.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Weil group.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Witt vector.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Zariski topology.</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Capuano, Laura, </subfield><subfield code="e">contributor.</subfield><subfield code="4">ctb</subfield><subfield code="4">https://id.loc.gov/vocabulary/relators/ctb</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Fuchs, Clemens, </subfield><subfield code="e">editor.</subfield><subfield code="4">edt</subfield><subfield code="4">http://id.loc.gov/vocabulary/relators/edt</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Gao, Ziyang, </subfield><subfield code="e">contributor.</subfield><subfield code="4">ctb</subfield><subfield code="4">https://id.loc.gov/vocabulary/relators/ctb</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Gorchinskiy, Sergey, </subfield><subfield code="e">contributor.</subfield><subfield code="4">ctb</subfield><subfield code="4">https://id.loc.gov/vocabulary/relators/ctb</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Jossen, Peter, </subfield><subfield code="e">contributor.</subfield><subfield code="4">ctb</subfield><subfield code="4">https://id.loc.gov/vocabulary/relators/ctb</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Kanel, Rafael von, </subfield><subfield code="e">contributor.</subfield><subfield code="4">ctb</subfield><subfield code="4">https://id.loc.gov/vocabulary/relators/ctb</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Karolus, Christina, </subfield><subfield code="e">contributor.</subfield><subfield code="4">ctb</subfield><subfield code="4">https://id.loc.gov/vocabulary/relators/ctb</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Kuhne, Lars, </subfield><subfield code="e">contributor.</subfield><subfield code="4">ctb</subfield><subfield code="4">https://id.loc.gov/vocabulary/relators/ctb</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Mocz, Lucia, </subfield><subfield code="e">contributor.</subfield><subfield code="4">ctb</subfield><subfield code="4">https://id.loc.gov/vocabulary/relators/ctb</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Veneziano, Francesco, </subfield><subfield code="e">contributor.</subfield><subfield code="4">ctb</subfield><subfield code="4">https://id.loc.gov/vocabulary/relators/ctb</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Wustholz, Gisbert, </subfield><subfield code="e">contributor.</subfield><subfield code="4">ctb</subfield><subfield code="4">https://id.loc.gov/vocabulary/relators/ctb</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Wüstholz, Gisbert, </subfield><subfield code="e">editor.</subfield><subfield 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