Development of iwasawa theory
Webcohomologies of the Hodge-Iwasawa modules we developed in our series papers on Hodge-Iwasawa theory. The corresponding cohomologies will be essential in the corresponding development of the contact with the corresponding Iwasawa theoretic consideration, while they are as well very crucial in the corresponding study of the … In number theory, Iwasawa theory is the study of objects of arithmetic interest over infinite towers of number fields. It began as a Galois module theory of ideal class groups, initiated by Kenkichi Iwasawa (1959) (岩澤 健吉), as part of the theory of cyclotomic fields. In the early 1970s, Barry Mazur considered … See more Let $${\displaystyle p}$$ be a prime number and let $${\displaystyle K=\mathbb {Q} (\mu _{p})}$$ be the field generated over $${\displaystyle \mathbb {Q} }$$ by the $${\displaystyle p}$$th roots of unity. Iwasawa … See more The Galois group of the infinite tower, the starting field, and the sort of arithmetic module studied can all be varied. In each case, there is a … See more • de Shalit, Ehud (1987), Iwasawa theory of elliptic curves with complex multiplication. p-adic L functions, Perspectives in Mathematics, vol. 3, Boston etc.: Academic Press, ISBN 978-0-12-210255-4, Zbl 0674.12004 See more From this beginning in the 1950s, a substantial theory has been built up. A fundamental connection was noticed between the module theory, and the p-adic L-functions that were defined in the 1960s by Kubota and Leopoldt. The latter begin from the See more • Ferrero–Washington theorem • Tate module of a number field See more • "Iwasawa theory", Encyclopedia of Mathematics, EMS Press, 2001 [1994] See more
Development of iwasawa theory
Did you know?
WebSelect search scope, currently: catalog all catalog, articles, website, & more in one search; catalog books, media & more in the Stanford Libraries' collections; articles+ journal articles & other e-resources http://staff.ustc.edu.cn/~yiouyang/iwasawa.pdf
WebJul 1, 2010 · Iwasawa theory provides a framework for studying these conjectures. In its essence, the idea is to study Selmer groups associated to a family of representations of the absolute Galois group of a number field. The formulation of these conjectures in a general setting leads to some fundamental problems. One problem is to find a simple way to ... WebJun 15, 2006 · Abstract. The 1995 work by Wiles and Taylor-Wiles opened up a whole new technique in algebraic number theory and, a decade on, the waves caused by this incredibly important work are still being felt. This book describes a generalization of their techniques to Hilbert modular forms (towards the proof of the celebrated ‘R=T’ theorem) and ...
Nov 1, 2024 ·
WebR. Greenberg’s pseudo-nullity conjecture in Iwasawa theory, to products in K-groups of cyclotomic integer rings, and to Y. Ihara’s pro-pLie algebra arising from the outer rep-resentation of Galois on the pro-pfundamental group of the projective line minus three points. In this paper, we focus instead on a relationship between the structure ...
WebNov 1, 2024 · Buy Development of Iwasawa Theory: The Centennial of K. Iwasawa's Birth (86) (Advanced Studies in Pure Mathematics, 86) on Amazon.com FREE SHIPPING on qualified orders Development of Iwasawa Theory: The Centennial of K. Iwasawa's Birth (86) (Advanced Studies in Pure Mathematics, 86): Kurihara, Masato, Bannai, Kenichi, … small wading pool ideasWebOct 26, 1998 · In 1952 Iwasawa published Theory of algebraic functions in Japanese. The book begins with an historical survey of the theory of algebraic functions of one variable, from analytical, algebraic geometrical, and algebro-arithmetical view points. small wading birdsWebJan 1, 2024 · Sign In Help small waffle fries chick fil a caloriesWebJan 1, 2024 · Abstract. We introduce a natural way to define Selmer groups and p p -adic L L -functions for modular forms of weight 1. The corresponding Galois representation ρ ρ of Gal(¯¯¯¯¯Q/Q) G a l ( Q ¯ / Q) is a 2-dimensional Artin representation with odd determinant. Thus, the dimension d+ d + of the (+1)-eigenspace for complex conjugation is 1. small wading poolshttp://blog.math.toronto.edu/GraduateBlog/files/2024/02/Debanjana_thesis.pdf small wading pools for kidsWebJul 1, 2024 · A theory of $\mathbf {Z} _ { p }$-extensions introduced by K. Iwasawa [a8]. Its motivation has been a strong analogy between number fields and curves over finite fields. One of the most fruitful results in this theory is the Iwasawa main conjecture, which has been proved for totally real number fields [a19]. The conjecture is considered as an ... small wader birdsWebKeywords and Phrases: Class field theory, reflection formula, weak Leopoldt conjecture, Iwasawa µ-invariant, uniform p-adic Lie exten-sion, p-adic Galois representation 1 Introduction This note is about two famous conjectures in Iwasawa theory and their de-pendencies. Throughout the article, we fix a rational prime p (which may be small waffle crochet stitch