Main conjecture of Iwasawa theory information

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...

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

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...

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...

mathematical finance. Iwasawa theory and the Main conjecture of Iwasawa theory Initially created by Kenkichi Iwasawa, Iwasawa theory was originally developed...

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

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...

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...

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

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...

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...

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...

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...

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...

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

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

Department of Mathematics at IIT Guwahati, India. He is known for his work related to arithmetic number theory, in particular applications to Iwasawa Theory and...

Urban is a professor of mathematics at Columbia University working in number theory and automorphic forms, particularly Iwasawa theory. Urban received his...