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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Superior document: | Title is part of eBook package: De Gruyter EBOOK PACKAGE COMPLETE 2019 English |
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Place / Publishing House: | Princeton, NJ : : Princeton University Press, , [2019] ©2019 |
Year of Publication: | 2019 |
Language: | English |
Series: | Annals of Mathematics Studies ;
202 |
Online Access: | |
Physical Description: | 1 online resource (186 p.) :; 1 b/w illus. |
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072 | 7 | |a MAT004000 |2 bisacsh | |
082 | 0 | 4 | |a 516.35 |2 23 |
245 | 0 | 0 | |a Arithmetic and Geometry : |b Ten Years in Alpbach (AMS-202) / |c ed. by Gisbert Wüstholz, Clemens Fuchs. |
264 | 1 | |a Princeton, NJ : |b Princeton University Press, |c [2019] | |
264 | 4 | |c ©2019 | |
300 | |a 1 online resource (186 p.) : |b 1 b/w illus. | ||
336 | |a text |b txt |2 rdacontent | ||
337 | |a computer |b c |2 rdamedia | ||
338 | |a online resource |b cr |2 rdacarrier | ||
347 | |a text file |b PDF |2 rda | ||
490 | 0 | |a Annals of Mathematics Studies ; |v 202 | |
505 | 0 | 0 | |t Frontmatter -- |t Contents -- |t Preface -- |t 1. Introduction -- |t 2. Local Shimura Varieties: Minicourse Given by Peter Scholze -- |t 3. Hyperelliptic Continued Fractions and Generalized Jacobians: Minicourse Given by Umberto Zannier -- |t 4. Faltings Heights and L-functions: Minicourse Given by Shou-Wu Zhang -- |t List of Contributors |
506 | 0 | |a restricted access |u http://purl.org/coar/access_right/c_16ec |f online access with authorization |2 star | |
520 | |a 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. | ||
530 | |a Issued also in print. | ||
538 | |a Mode of access: Internet via World Wide Web. | ||
546 | |a In English. | ||
588 | 0 | |a Description based on online resource; title from PDF title page (publisher's Web site, viewed 31. Jan 2022) | |
650 | 0 | |a Arithmetical algebraic geometry. | |
650 | 7 | |a MATHEMATICS / Arithmetic. |2 bisacsh | |
653 | |a Abelian variety. | ||
653 | |a Algebraic geometry. | ||
653 | |a Algebraic independence. | ||
653 | |a Algebraic space. | ||
653 | |a Analytic number theory. | ||
653 | |a Arbitrarily large. | ||
653 | |a Automorphic form. | ||
653 | |a Automorphism. | ||
653 | |a Base change. | ||
653 | |a Big O notation. | ||
653 | |a Class number formula. | ||
653 | |a Cohomology. | ||
653 | |a Complex multiplication. | ||
653 | |a Computation. | ||
653 | |a Conjecture. | ||
653 | |a Conjugacy class. | ||
653 | |a Continued fraction. | ||
653 | |a Cusp form. | ||
653 | |a Diagram (category theory). | ||
653 | |a Dimension. | ||
653 | |a Diophantine equation. | ||
653 | |a Diophantine geometry. | ||
653 | |a Discriminant. | ||
653 | |a Divisible group. | ||
653 | |a Double coset. | ||
653 | |a Eisenstein series. | ||
653 | |a Endomorphism. | ||
653 | |a Equation. | ||
653 | |a Existential quantification. | ||
653 | |a Exponential map (Riemannian geometry). | ||
653 | |a Fiber bundle. | ||
653 | |a Floor and ceiling functions. | ||
653 | |a Formal group. | ||
653 | |a Formal power series. | ||
653 | |a Formal scheme. | ||
653 | |a Fundamental group. | ||
653 | |a Geometric Langlands correspondence. | ||
653 | |a Geometry. | ||
653 | |a Heegner point. | ||
653 | |a Hodge structure. | ||
653 | |a Hodge theory. | ||
653 | |a Homomorphism. | ||
653 | |a I0. | ||
653 | |a Integer. | ||
653 | |a Intersection number. | ||
653 | |a Irreducible component. | ||
653 | |a Isogeny. | ||
653 | |a Isomorphism class. | ||
653 | |a Jacobian variety. | ||
653 | |a L-function. | ||
653 | |a Langlands dual group. | ||
653 | |a Laurent series. | ||
653 | |a Linear combination. | ||
653 | |a Local system. | ||
653 | |a Logarithmic derivative. | ||
653 | |a Logarithmic form. | ||
653 | |a Mathematics. | ||
653 | |a Modular form. | ||
653 | |a Moduli space. | ||
653 | |a Monotonic function. | ||
653 | |a Natural topology. | ||
653 | |a P-adic analysis. | ||
653 | |a P-adic number. | ||
653 | |a Pell's equation. | ||
653 | |a Perverse sheaf. | ||
653 | |a Polylogarithm. | ||
653 | |a Polynomial. | ||
653 | |a Power series. | ||
653 | |a Presheaf (category theory). | ||
653 | |a Prime number. | ||
653 | |a Projective space. | ||
653 | |a Quaternion algebra. | ||
653 | |a Rational point. | ||
653 | |a Real number. | ||
653 | |a Reductive group. | ||
653 | |a Rigid analytic space. | ||
653 | |a Roth's theorem. | ||
653 | |a Series expansion. | ||
653 | |a Shafarevich conjecture. | ||
653 | |a Sheaf (mathematics). | ||
653 | |a Shimura variety. | ||
653 | |a Siegel zero. | ||
653 | |a Special case. | ||
653 | |a Stack (mathematics). | ||
653 | |a Subset. | ||
653 | |a Summation. | ||
653 | |a Szpiro's conjecture. | ||
653 | |a Tate conjecture. | ||
653 | |a Tate module. | ||
653 | |a Taylor series. | ||
653 | |a Theorem. | ||
653 | |a Theta function. | ||
653 | |a Topological ring. | ||
653 | |a Topology. | ||
653 | |a Torsor (algebraic geometry). | ||
653 | |a Upper and lower bounds. | ||
653 | |a Vector bundle. | ||
653 | |a Weil group. | ||
653 | |a Witt vector. | ||
653 | |a Zariski topology. | ||
700 | 1 | |a Capuano, Laura, |e contributor. |4 ctb |4 https://id.loc.gov/vocabulary/relators/ctb | |
700 | 1 | |a Fuchs, Clemens, |e editor. |4 edt |4 http://id.loc.gov/vocabulary/relators/edt | |
700 | 1 | |a Gao, Ziyang, |e contributor. |4 ctb |4 https://id.loc.gov/vocabulary/relators/ctb | |
700 | 1 | |a Gorchinskiy, Sergey, |e contributor. |4 ctb |4 https://id.loc.gov/vocabulary/relators/ctb | |
700 | 1 | |a Jossen, Peter, |e contributor. |4 ctb |4 https://id.loc.gov/vocabulary/relators/ctb | |
700 | 1 | |a Kanel, Rafael von, |e contributor. |4 ctb |4 https://id.loc.gov/vocabulary/relators/ctb | |
700 | 1 | |a Karolus, Christina, |e contributor. |4 ctb |4 https://id.loc.gov/vocabulary/relators/ctb | |
700 | 1 | |a Kuhne, Lars, |e contributor. |4 ctb |4 https://id.loc.gov/vocabulary/relators/ctb | |
700 | 1 | |a Mocz, Lucia, |e contributor. |4 ctb |4 https://id.loc.gov/vocabulary/relators/ctb | |
700 | 1 | |a Veneziano, Francesco, |e contributor. |4 ctb |4 https://id.loc.gov/vocabulary/relators/ctb | |
700 | 1 | |a Wustholz, Gisbert, |e contributor. |4 ctb |4 https://id.loc.gov/vocabulary/relators/ctb | |
700 | 1 | |a Wüstholz, Gisbert, |e editor. |4 edt |4 http://id.loc.gov/vocabulary/relators/edt | |
773 | 0 | 8 | |i Title is part of eBook package: |d De Gruyter |t EBOOK PACKAGE COMPLETE 2019 English |z 9783110610765 |
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773 | 0 | 8 | |i Title is part of eBook package: |d De Gruyter |t EBOOK PACKAGE Mathematics 2019 English |z 9783110610406 |
773 | 0 | 8 | |i Title is part of eBook package: |d De Gruyter |t EBOOK PACKAGE Mathematics 2019 |z 9783110606362 |o ZDB-23-DMA |
773 | 0 | 8 | |i Title is part of eBook package: |d De Gruyter |t Princeton Annals of Mathematics eBook-Package 1940-2020 |z 9783110494914 |o ZDB-23-PMB |
773 | 0 | 8 | |i Title is part of eBook package: |d De Gruyter |t Princeton University Press Complete eBook-Package 2019 |z 9783110663365 |
776 | 0 | |c print |z 9780691193786 | |
856 | 4 | 0 | |u https://doi.org/10.1515/9780691197548?locatt=mode:legacy |
856 | 4 | 0 | |u https://www.degruyter.com/isbn/9780691197548 |
856 | 4 | 2 | |3 Cover |u https://www.degruyter.com/document/cover/isbn/9780691197548/original |
912 | |a 978-3-11-061040-6 EBOOK PACKAGE Mathematics 2019 English |b 2019 | ||
912 | |a 978-3-11-061076-5 EBOOK PACKAGE COMPLETE 2019 English |b 2019 | ||
912 | |a 978-3-11-066336-5 Princeton University Press Complete eBook-Package 2019 |b 2019 | ||
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