Arithmetic Moduli of Elliptic Curves. (AM-108), Volume 108 / / Barry Mazur, Nicholas M. Katz.
This work is a comprehensive treatment of recent developments in the study of elliptic curves and their moduli spaces. The arithmetic study of the moduli spaces began with Jacobi's "Fundamenta Nova" in 1829, and the modern theory was erected by Eichler-Shimura, Igusa, and Deligne-Rapo...
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Katz, Nicholas M., author. aut http://id.loc.gov/vocabulary/relators/aut Arithmetic Moduli of Elliptic Curves. (AM-108), Volume 108 / Barry Mazur, Nicholas M. Katz. Princeton, NJ : Princeton University Press, [2016] ©1985 1 online resource (528 p.) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Annals of Mathematics Studies ; 108 Frontmatter -- TABLE OF CONTENTS -- INTRODUCTION -- Chapter 1. GENERALITIES ON " A-STRUCTURES" AND " A-GENERATORS" -- Chapter 2. REVIEW OF ELLIPTIC CURVES -- Chapter 3. THE FOUR BASIC MODULI PROBLEMS FOR ELLIPTIC CURVES: SORITES -- Chapter 4. THE FORMALISM OF MODULI PROBLEMS -- Chapter 5. REGULARITY THEOREMS -- Chapter 6. CYCLICITY -- Chapter 7. QUOTIENTS BY FINITE GROUPS -- Chapter 8. COARSE MODULI SCHEMES, CUSPS, AND COMPACTIFICATION -- Chapter 9. MODULI PROBLEMS VIEWED OVER CYCLOTOMIC INTEGER RINGS -- Chapter 10. THE CALCULUS OF CUSPS AND COMPONENTS VIA THE GROUPS T[N], AND THE GLOBAL STRUCTURE OF THE BASIC MODULI PROBLEMS -- Chapter 11. INTERLUDE-EXOTIC MODULAR MORPHISMS AND ISOMORPHISMS -- Chapter 12. NEW MODULI PROBLEMS IN CHARACTERISTIC p; IGUSA CURVES -- Chapter 13. REDUCTIONS mod p OF THE BASIC MODULI PROBLEMS -- Chapter 14. APPLICATION TO THEOREMS OF GOOD REDUCTION -- NOTES ADDED IN PROOF -- REFERENCES restricted access http://purl.org/coar/access_right/c_16ec online access with authorization star This work is a comprehensive treatment of recent developments in the study of elliptic curves and their moduli spaces. The arithmetic study of the moduli spaces began with Jacobi's "Fundamenta Nova" in 1829, and the modern theory was erected by Eichler-Shimura, Igusa, and Deligne-Rapoport. In the past decade mathematicians have made further substantial progress in the field. This book gives a complete account of that progress, including not only the work of the authors, but also that of Deligne and Drinfeld. 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) Curves, Elliptic. Geometry, Algebraic. Moduli theory. MATHEMATICS / Geometry / Algebraic. bisacsh Abelian variety. Addition. Algebraic variety. Algebraically closed field. Ambient space. Arithmetic. Axiom. Barry Mazur. Base change. Calculation. Canonical map. Change of base. Closed immersion. Coefficient. Coherent sheaf. Cokernel. Commutative property. Congruence relation. Coprime integers. Corollary. Cusp form. Cyclic group. Dense set. Diagram (category theory). Dimension. Discrete valuation ring. Disjoint union. Divisor. Eigenfunction. Elliptic curve. Empty set. Factorization. Field of fractions. Finite field. Finite group. Finite morphism. Free module. Functor. Group (mathematics). Integer. Irreducible component. Level structure. Local ring. Maximal ideal. Modular curve. Modular equation. Modular form. Moduli space. Morphism of schemes. Morphism. Neighbourhood (mathematics). Noetherian. One-parameter group. Open problem. Prime factor. Prime number. Prime power. Q.E.D. Regularity theorem. Representation theory. Residue field. Riemann hypothesis. Smoothness. Special case. Subgroup. Subring. Subset. Theorem. Topology. Two-dimensional space. Zariski topology. Mazur, Barry, author. aut http://id.loc.gov/vocabulary/relators/aut 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 eBook-Package Archive 1927-1999 9783110442496 print 9780691083520 https://doi.org/10.1515/9781400881710 https://www.degruyter.com/isbn/9781400881710 Cover https://www.degruyter.com/document/cover/isbn/9781400881710/original |
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English |
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author |
Katz, Nicholas M., Katz, Nicholas M., Mazur, Barry, |
spellingShingle |
Katz, Nicholas M., Katz, Nicholas M., Mazur, Barry, Arithmetic Moduli of Elliptic Curves. (AM-108), Volume 108 / Annals of Mathematics Studies ; Frontmatter -- TABLE OF CONTENTS -- INTRODUCTION -- Chapter 1. GENERALITIES ON " A-STRUCTURES" AND " A-GENERATORS" -- Chapter 2. REVIEW OF ELLIPTIC CURVES -- Chapter 3. THE FOUR BASIC MODULI PROBLEMS FOR ELLIPTIC CURVES: SORITES -- Chapter 4. THE FORMALISM OF MODULI PROBLEMS -- Chapter 5. REGULARITY THEOREMS -- Chapter 6. CYCLICITY -- Chapter 7. QUOTIENTS BY FINITE GROUPS -- Chapter 8. COARSE MODULI SCHEMES, CUSPS, AND COMPACTIFICATION -- Chapter 9. MODULI PROBLEMS VIEWED OVER CYCLOTOMIC INTEGER RINGS -- Chapter 10. THE CALCULUS OF CUSPS AND COMPONENTS VIA THE GROUPS T[N], AND THE GLOBAL STRUCTURE OF THE BASIC MODULI PROBLEMS -- Chapter 11. INTERLUDE-EXOTIC MODULAR MORPHISMS AND ISOMORPHISMS -- Chapter 12. NEW MODULI PROBLEMS IN CHARACTERISTIC p; IGUSA CURVES -- Chapter 13. REDUCTIONS mod p OF THE BASIC MODULI PROBLEMS -- Chapter 14. APPLICATION TO THEOREMS OF GOOD REDUCTION -- NOTES ADDED IN PROOF -- REFERENCES |
author_facet |
Katz, Nicholas M., Katz, Nicholas M., Mazur, Barry, Mazur, Barry, Mazur, Barry, |
author_variant |
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author_role |
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author2 |
Mazur, Barry, Mazur, Barry, |
author2_variant |
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author2_role |
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author_sort |
Katz, Nicholas M., |
title |
Arithmetic Moduli of Elliptic Curves. (AM-108), Volume 108 / |
title_full |
Arithmetic Moduli of Elliptic Curves. (AM-108), Volume 108 / Barry Mazur, Nicholas M. Katz. |
title_fullStr |
Arithmetic Moduli of Elliptic Curves. (AM-108), Volume 108 / Barry Mazur, Nicholas M. Katz. |
title_full_unstemmed |
Arithmetic Moduli of Elliptic Curves. (AM-108), Volume 108 / Barry Mazur, Nicholas M. Katz. |
title_auth |
Arithmetic Moduli of Elliptic Curves. (AM-108), Volume 108 / |
title_alt |
Frontmatter -- TABLE OF CONTENTS -- INTRODUCTION -- Chapter 1. GENERALITIES ON " A-STRUCTURES" AND " A-GENERATORS" -- Chapter 2. REVIEW OF ELLIPTIC CURVES -- Chapter 3. THE FOUR BASIC MODULI PROBLEMS FOR ELLIPTIC CURVES: SORITES -- Chapter 4. THE FORMALISM OF MODULI PROBLEMS -- Chapter 5. REGULARITY THEOREMS -- Chapter 6. CYCLICITY -- Chapter 7. QUOTIENTS BY FINITE GROUPS -- Chapter 8. COARSE MODULI SCHEMES, CUSPS, AND COMPACTIFICATION -- Chapter 9. MODULI PROBLEMS VIEWED OVER CYCLOTOMIC INTEGER RINGS -- Chapter 10. THE CALCULUS OF CUSPS AND COMPONENTS VIA THE GROUPS T[N], AND THE GLOBAL STRUCTURE OF THE BASIC MODULI PROBLEMS -- Chapter 11. INTERLUDE-EXOTIC MODULAR MORPHISMS AND ISOMORPHISMS -- Chapter 12. NEW MODULI PROBLEMS IN CHARACTERISTIC p; IGUSA CURVES -- Chapter 13. REDUCTIONS mod p OF THE BASIC MODULI PROBLEMS -- Chapter 14. APPLICATION TO THEOREMS OF GOOD REDUCTION -- NOTES ADDED IN PROOF -- REFERENCES |
title_new |
Arithmetic Moduli of Elliptic Curves. (AM-108), Volume 108 / |
title_sort |
arithmetic moduli of elliptic curves. (am-108), volume 108 / |
series |
Annals of Mathematics Studies ; |
series2 |
Annals of Mathematics Studies ; |
publisher |
Princeton University Press, |
publishDate |
2016 |
physical |
1 online resource (528 p.) Issued also in print. |
contents |
Frontmatter -- TABLE OF CONTENTS -- INTRODUCTION -- Chapter 1. GENERALITIES ON " A-STRUCTURES" AND " A-GENERATORS" -- Chapter 2. REVIEW OF ELLIPTIC CURVES -- Chapter 3. THE FOUR BASIC MODULI PROBLEMS FOR ELLIPTIC CURVES: SORITES -- Chapter 4. THE FORMALISM OF MODULI PROBLEMS -- Chapter 5. REGULARITY THEOREMS -- Chapter 6. CYCLICITY -- Chapter 7. QUOTIENTS BY FINITE GROUPS -- Chapter 8. COARSE MODULI SCHEMES, CUSPS, AND COMPACTIFICATION -- Chapter 9. MODULI PROBLEMS VIEWED OVER CYCLOTOMIC INTEGER RINGS -- Chapter 10. THE CALCULUS OF CUSPS AND COMPONENTS VIA THE GROUPS T[N], AND THE GLOBAL STRUCTURE OF THE BASIC MODULI PROBLEMS -- Chapter 11. INTERLUDE-EXOTIC MODULAR MORPHISMS AND ISOMORPHISMS -- Chapter 12. NEW MODULI PROBLEMS IN CHARACTERISTIC p; IGUSA CURVES -- Chapter 13. REDUCTIONS mod p OF THE BASIC MODULI PROBLEMS -- Chapter 14. APPLICATION TO THEOREMS OF GOOD REDUCTION -- NOTES ADDED IN PROOF -- REFERENCES |
isbn |
9781400881710 9783110494914 9783110442496 9780691083520 |
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Q - Science |
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QA - Mathematics |
callnumber-label |
QA567 |
callnumber-sort |
QA 3567 |
url |
https://doi.org/10.1515/9781400881710 https://www.degruyter.com/isbn/9781400881710 https://www.degruyter.com/document/cover/isbn/9781400881710/original |
illustrated |
Not Illustrated |
dewey-hundreds |
500 - Science |
dewey-tens |
510 - Mathematics |
dewey-ones |
516 - Geometry |
dewey-full |
516.3/5 |
dewey-sort |
3516.3 15 |
dewey-raw |
516.3/5 |
dewey-search |
516.3/5 |
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10.1515/9781400881710 |
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Arithmetic Moduli of Elliptic Curves. (AM-108), Volume 108 / |
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