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Elliptic Curves and Arithmetic Invariants 2013 ed. [Minkštas viršelis]

  • Formatas: Paperback / softback, 450 pages, aukštis x plotis: 235x155 mm, weight: 7022 g, XVIII, 450 p., 1 Paperback / softback
  • Serija: Springer Monographs in Mathematics
  • Išleidimo metai: 08-Feb-2015
  • Leidėjas: Springer-Verlag New York Inc.
  • ISBN-10: 1489990925
  • ISBN-13: 9781489990921
Kitos knygos pagal šią temą:
Elliptic Curves and Arithmetic Invariants 2013 ed.Didesnis paveikslėlis
  • Formatas: Paperback / softback, 450 pages, aukštis x plotis: 235x155 mm, weight: 7022 g, XVIII, 450 p., 1 Paperback / softback
  • Serija: Springer Monographs in Mathematics
  • Išleidimo metai: 08-Feb-2015
  • Leidėjas: Springer-Verlag New York Inc.
  • ISBN-10: 1489990925
  • ISBN-13: 9781489990921
Kitos knygos pagal šią temą:
Pastovi nuoroda: https://www.kriso.lt/db/9781489990921.html
Raktažodžiai:
This introduction to Shimura varieties covers key topics including non-triviality of arithmetic invariants and special values of L-functions; elliptic curves over complex and p-adic fields; Hecke algebras; elliptic and modular curves over rings and more.

This introduction to Shimura varieties covers key topics including non-triviality of arithmetic invariants and special values of L-functions; elliptic curves over complex and p-adic fields; Hecke algebras; elliptic and modular curves over rings and more.

This book contains a detailed account of the result of the author's recent Annals paper and JAMS paper on arithmetic invariant, includingµ-invariant, L-invariant, and similar topics. This book can be regarded as an introductory text to the author's previous bookp-Adic Automorphic Forms on Shimura Varieties. Written as a down-to-earth introduction to Shimura varieties, this text includes many examples and applications of the theory that provide motivation for the reader. Since it is limited to modular curves and the corresponding Shimura varieties, this book is not only a great resource for experts in the field, but it is also accessible to advanced graduate students studying number theory. Key topics include non-triviality of arithmetic invariants and special values of L-functions; elliptic curves over complex and p-adic fields; Hecke algebras; scheme theory; elliptic and modular curves over rings; and Shimura curves.

Recenzijos

The main aim of the book is to give an account of Hidas results on arithmetic invariants in an accessible way. The book is intended for mathematicians with some background on modular forms and is worthwhile for both graduate students and experts. There are numerous examples, exercises, and remarks, all aimed at carefully helping the reader. In conclusion, this book is a very welcome addition to the mathematical literature. (Florian Sprung, Mathematical Reviews, April, 2015)

The author gives in this book a detailed account of results concerning arithmetic invariants, including µ-invariant and L-invariant. it contains a detailed account of the authors recent results concerning arithmetic invariants. The book, addressed to advanced graduate students and experts working in number theory and arithmetic geometry, is a welcome addition to this beautiful and difficult area of research. (Andrzej Dbrowski, zbMATH, Vol. 1284, 2014)

1 Non-triviality of Arithmetic Invariants.- 2 Elliptic Curves and
Modular Forms.- 3 Invariants, Shimura Variety and Hecke Algebra.- 4 Review of
Scheme Theory.- 5 Geometry of Variety.- 6 Elliptic and Modular Curves over
Rings.- 7 Modular Curves as Shimura Variety.- 8 Non-vanishing Modulo p of
Hecke Lvalues.- 9 p-Adic Hecke L-functions and their -invariants.- 10 Toric
Subschemes in a Split Formal Torus.- 11 Hecke Stable Subvariety is a Shimura
Subvariety.- References.- Symbol Index.- Statement Index.- Subject Index.
Haruzo Hida is currently a professor of mathematics at University of California, Los Angeles.