In mathematics, the main conjecture of Iwasawa theory is a deep relationship between p-adic L-functions and ideal class groups of cyclotomic fields, proved...

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...

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

the p-parity theorem of Nekovář (2009) and Dokchitser & Dokchitser (2010) and with the proof of the main conjecture of Iwasawa theory for GL(2) by Skinner...

becoming a professor at the Indian Institute of Science in 2019. Kakde proved the main conjecture of Iwasawa theory in the totally real μ = 0 case. Together...

main conjecture of Iwasawa theory for that situation. Such conjectures represent formal statements concerning the philosophy that special values of L-functions...

Iwasawa theory. He further worked with Barry Mazur on the main conjecture of Iwasawa theory over the rational numbers, and soon afterward, he generalised...

in conjectures on special values of L-functions and the formulation of a non-commutative main conjecture of Iwasawa theory and in construction of higher...

Goss zeta functions of function fields have a Riemann hypothesis, proved by Sheats (1998). The main conjecture of Iwasawa theory, proved by Barry Mazur...

such as the finiteness of some Tate-Shafarevich groups. This led to Karl Rubin's new proof of the main conjecture of Iwasawa theory, considered simpler than...

order to prove the main conjecture of Iwasawa theory, a corollary of which is a strengthening of the Herbrand–Ribet theorem: the power of p dividing Bp−n...

In number theory, Fermat's Last Theorem (sometimes called Fermat's conjecture, especially in older texts) states that no three positive integers a, b...

this conjecture has been made as a consequence of work on Iwasawa theory, and in particular of the proofs given for the so-called "main conjecture of Iwasawa...

Popescu, Cristian (2015). "An equivariant main conjecture in Iwasawa theory and applications". Journal of Algebraic Geometry. 24 (4): 629–692. arXiv:1103...

worked 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...

of Kähler manifolds discovered by Heisuke Hironaka. Iwasawa theory and the Main conjecture of Iwasawa theory — Initially created by Kenkichi Iwasawa,...

Neukirch, Masatoshi Gündüz Ikeda, Kenkichi Iwasawa, and Kôji Uchida (Neukirch–Uchida theorem, 1969), prior to conjectures made about hyperbolic curves over number...

number conjecture (ETNC) has been formulated, to consolidate the connection of these ideas with Iwasawa theory, and its so-called Main Conjecture. All of these...

1900–1950. 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...

the anticyclotomic main conjecture of Iwasawa theory, special values of L-functions, and Serre-type conjectures for symplectic groups. Harris, Michael;...

corollary of their work on the main conjecture of Iwasawa theory. Kolyvagin (1990) later gave a simpler proof using Euler systems. A version of the Gras...

work. Skinner and Eric Urban proved many cases of Iwasawa–Greenberg main conjectures for a large class of modular forms. As a consequence, for a modular...

non-commutative version of the main conjecture of Iwasawa theory, on which much of the foundation of this important subject is based. Iwasawa theory has its origins...

modern algebraic geometry such as the category of schemes, significant number theoretic ideas from Iwasawa theory, and other 20th-century techniques which were...

conjecture, the Coates-Sinnott conjecture, and a recently developed equivariant version of the main conjecture in Iwasawa theory. Solomon, David (2010). "Equivariant...

number fields, the BSD conjecture for number fields, and Iwasawa theory for number fields use very explicit but narrow class field theory methods or their generalizations...

completed a senior honors thesis entitled The Main Conjecture of Iwasawa Theory under the supervision of Noam Elkies. After college, Ho won a Harvard Herchel...

parts of number theory and algebraic geometry. Much of the theory is in the form of proposed conjectures, which can be related at various levels of generality...

the "main conjectures" of Iwasawa and Barry Mazur to this setting. He has since generalized this setup to present Iwasawa theory as the theory of p-adic...

the development of Iwasawa theory and the Main Conjecture. The proof of the fundamental lemma in the Langlands program also made use of techniques that...