This book provides a comprehensive account of a key, perhaps the most important, theory that forms the basis of Taylor-Wiles proof of Fermat's last theorem. Hida begins with an overview of the theory of automorphic forms on linear algebraic groups and then covers the basic theory and recent results on elliptic modular forms, including a substantial simplification of the Taylor-Wiles proof by Fujiwara and Diamond. He offers a detailed exposition of the representation theory of profinite groups (including deformation theory), as well as the Euler characteristic formulas of Galois cohomology groups. The final chapter presents a proof of a non-abelian class number formula.
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Book Description
This book provides a comprehensive account of the key theory upon which the Taylor-Wiles proof of Fermat's last theorem is based. It begins with an overview of the theory of automorphic forms on linear algebraic groups and covers the basic theory and recent results on elliptic modular forms. It includes a detailed exposition of the representation theory of profinite groups and contains several new results from the author. The book will appeal to graduate students and researchers in number theory (including algebraic and analytic number theorists) and arithmetic algebraic geometry.
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Inside This Book
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First Sentence:
It is difficult to provide a brief summary of techniques used in modern number theory. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
injective presentation, strong multiplicity one theorem, universal deformation ring, universal couple, upper triangular representation, characteristic power series, valuation ring finite, profinite group, class number formula, global class field theory, deformation rings, integer ring, reciprocity map, open normal subgroups, cyclotomic character, local class field theory, surjective isomorphism, control theorem, profinite topology, following exact sequence, extension unramified, absolute irreducibility, cusp forms, adele ring, inertia group Key Phrases - Capitalized Phrases (CAPs): (learn more)
Proof Let, Modular Forins, Bloch-Kato Selmer New!
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Front Cover | Table of Contents | First Pages | Index | Surprise Me!
It is difficult to provide a brief summary of techniques used in modern number theory. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
injective presentation, strong multiplicity one theorem, universal deformation ring, universal couple, upper triangular representation, characteristic power series, valuation ring finite, profinite group, class number formula, global class field theory, deformation rings, integer ring, reciprocity map, open normal subgroups, cyclotomic character, local class field theory, surjective isomorphism, control theorem, profinite topology, following exact sequence, extension unramified, absolute irreducibility, cusp forms, adele ring, inertia group Key Phrases - Capitalized Phrases (CAPs): (learn more)
Proof Let, Modular Forins, Bloch-Kato Selmer New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Surprise Me!
Citations (learn more)
This book cites 19
books:
See all 19 books this book cites
4
books
cite this book:
- Class Field Theory (Advanced Book Classics) by Emil Artin in Back Matter
- Local Fields (London Mathematical Society Student Texts) by J. W. S. Cassels in Back Matter
- Algebraic Number Theory (Cambridge Studies in Advanced Mathematics) by A. Fröhlich in Back Matter
- Representations of Algebraic Groups (Mathematical Surveys and Monographs) by Jens Carsten Jantzen in Back Matter
- Class Field Theory (Grundlehren Der Math Wissenschaften, Band 280) by J. Neukirch in Back Matter
See all 19 books this book cites
- Doing Mathematics: Convention, Subject, Calculation, Analogy by Martin H. Krieger in Back Matter (1), and Back Matter (2)
- Arithmetic Geometry And Number Theory (Number Theory and Its Applications) by Lin Weg on page 386
- p-Adic Automorphic Forms on Shimura Varieties (Springer Monographs in Mathematics) by Haruzo Hida in Back Matter
- Hilbert Modular Forms and Iwasawa Theory (Oxford Mathematical Monographs) by Haruzo Hida in Back Matter
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