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...

conjecture of Iwasawa theory is a deep relationship between p-adic L-functions and ideal class groups of cyclotomic fields, proved by Kenkichi Iwasawa for primes...

Japanese mathematician who is known for his influence on algebraic number theory. Iwasawa was born in Shinshuku-mura, a town near Kiryū, in Gunma Prefecture...

theorem Hasse norm theorem Artin reciprocity Local class field theory Iwasawa theory Herbrand–Ribet theorem Vandiver's conjecture Stickelberger's theorem...

curves and modular forms, starting with Barry Mazur's generalizations of Iwasawa theory. In the early 1980s, Wiles spent a few years at the University of Cambridge...

ring of integers. Kenkichi Iwasawa independently discovered essentially the same method (without an analog of the local theory in Tate's thesis) during...

as the category of schemes, significant number theoretic ideas from Iwasawa theory, and other 20th-century techniques which were not available to Fermat...

to 1 in many programming languages. In lambda calculus and computability theory, natural numbers are represented by Church encoding as functions, where...

Intersection theory — Invariant theory — Iwasawa theory — K-theory — KK-theory — Knot theory — L-theory — Lie theory — Littlewood–Paley theory — Matrix theory —...

An example of an active area of research in algebraic number theory is Iwasawa theory. The Langlands program, one of the main current large-scale research...

explicit class field theory is used in many subareas of algebraic number theory such as Iwasawa theory and Galois modules theory. Most main achievements...

of DPMMS from 1991 to 1997. His research interests included Iwasawa theory, number theory and arithmetical algebraic geometry. He served on the Mathematical...

significant breakthrough on Galois theory: 251–253, 259  before switching to an attempt to extend horizontal Iwasawa theory for the inductive argument around...

Commutative Iwasawa algebras were introduced by Iwasawa (1959) in his study of Zp extensions in Iwasawa theory, and non-commutative Iwasawa algebras of...

L-functions and the formulation of a non-commutative main conjecture of Iwasawa theory and in construction of higher regulators. Parshin's conjecture concerns...

Indian Institute of Science in 2019. Kakde proved the main conjecture of Iwasawa theory in the totally real μ = 0 case. Together with Samit Dasgupta and Kevin...

elements. Also in set theory, 0 is the lowest ordinal number, corresponding to the empty set viewed as a well-ordered set. In order theory (and especially its...

Ramdorai (born 1962) is an algebraic number theorist known for her work on Iwasawa theory. She is a professor of mathematics and Canada Research Chair at University...

Dokchitser & Dokchitser (2010) and with the proof of the main conjecture of Iwasawa theory for GL(2) by Skinner & Urban (2014), they conclude that a positive proportion...

groups were obtained by Jürgen Neukirch, Masatoshi Gündüz Ikeda, Kenkichi Iwasawa, and Kôji Uchida (Neukirch–Uchida theorem, 1969), prior to conjectures...

theory Hodge theory Homology theory Homotopy theory Ideal theory Index theory Information theory Intersection theory Invariant theory Iwasawa theory K-theory...

groups. This led to Karl Rubin's new proof of the main conjecture of Iwasawa theory, considered simpler than the original proof due to Barry Mazur and Andrew...

arithmetic data of the Galois module involved. The main conjecture of Iwasawa theory (now a theorem due to Barry Mazur and Andrew Wiles) is the statement...

ISBN 978-1-56159-263-0. Bouganis, Thanasis; Venjakob, Otmar, eds. (2014). Iwasawa Theory 2012: State of the Art and Recent Advances. Springer. p. vii. ISBN 978-3-642-55245-8...

known for his work related to arithmetic number theory, in particular applications to Iwasawa Theory and p-adic measures. He has also published articles...

Heisuke Hironaka. Iwasawa theory and the Main conjecture of Iwasawa theory — Initially created by Kenkichi Iwasawa, Iwasawa theory was originally developed...

Université Sorbonne Paris Nord working in number theory and automorphic forms, particularly Iwasawa theory. Tilouine received his PhD in mathematics from...

mathematics, the Iwasawa conjecture may be: the main conjecture of Iwasawa theory the Ferrero–Washington theorem about the vanishing of Iwasawa's μ-invariant...

together on the main conjecture of Iwasawa theory. In an expository paper, Number Theory as Gadfly, Mazur describes number theory as a field which "produces,...

{\displaystyle \mathbb {Q} } is sometimes called a rational integer. Iwasawa Iwasawa theory Langlands Langlands program least common multiple The least common...