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20082024
most citedThe main conjecture of Iwasawa theory for totally real fields

7 citations · 31 across the 18 of their papers we have counts for

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math.NT2024

Ranks of Matrices of Logarithms of Algebraic Numbers II: The Matrix Coefficient Conjecture

Samit Dasgupta, Mahesh Kakde

Many questions in number theory concern the nonvanishing of determinants of square matrices of logarithms (complex or p-adic) of algebraic numbers. We present a new conjecture that…

math.NT2023

On The Equivariant Tamagawa Number Conjecture

Samit Dasgupta, Mahesh Kakde, Jesse Silliman

Let be a totally real field and a finite abelian CM extension of . Using class field theory, we show that our previous result giving a strong form of the Brumer-Stark co…

math.NT2023

The Residually Indistinguishable Case of Ribet's Method for GL2

Samit Dasgupta, Mahesh Kakde, Jesse Silliman +1

Ribet's method provides a strategy for constructing a nontrivial extension of a -adic Galois representation by another such representation . Suppose we are working ov…

math.NT2023

The Brumer--Stark Conjecture over Z

Samit Dasgupta, Mahesh Kakde, Jesse Silliman +1

In this paper we give a complete proof of the Brumer-Stark conjecture over .

math.NT2022

On the Brumer-Stark Conjecture and Refinements

Samit Dasgupta, Mahesh Kakde

We state the Brumer-Stark conjecture and motivate it from two perspectives. Stark's perspective arose in his attempts to generalize the classical Dirichlet class number formula for…

math.NT2021★ 1 cited

Brumer-Stark Units and Explicit Class Field Theory

Samit Dasgupta, Mahesh Kakde

Let be a totally real field of degree and an odd prime. We prove the -part of the integral Gross--Stark conjecture for the Brumer--Stark -units living in CM abeli…

math.NT2020★ 5 cited

On the Brumer-Stark Conjecture

Samit Dasgupta, Mahesh Kakde

Let be a finite abelian extension of number fields with totally real and a CM field. Let and be disjoint finite sets of places of satisfying the standard…

math.NT2020

On Constant Terms of Eisenstein Series

Samit Dasgupta, Mahesh Kakde

We calculate the constant terms of certain Hilbert modular Eisenstein series at all cusps. Our formula relates these constant terms to special values of Hecke -series. This buil…

math.NT2019★ 1 cited

Exterior powers in Iwasawa theory

F. Bleher, T. Chinburg, R. Greenberg +3

The Iwasawa theory of CM fields has traditionally concerned Iwasawa modules that are abelian pro-p Galois groups with ramification allowed at a maximal set of primes over p such th…

math.NT2018

A Note on the Main Conjecture over Q

Mahesh Kakde, Zdzislaw Wojtkowiak

In this note we show how the main conjecture of the Iwasawa theory over Q has a natural place in the context of the Galois representation of the Galois group on the…

math.NT2018★ 1 cited

On a refinement of the Birch and Swinnerton-Dyer Conjecture in positive characteristic

David Burns, Mahesh Kakde, Wansu Kim

We formulate a refined version of the Birch and Swinnerton-Dyer conjecture for abelian varieties over global function fields. This refinement incorporates both families of congruen…

math.NT2017★ 3 cited

Cup products in the etale cohomology of number fields

Frauke M. Bleher, Ted Chinburg, Ralph Greenberg +3

This paper concerns cup product pairings in étale cohomology related to work of M. Kim and of W. McCallum and R. Sharifi. We will show that by considering Ext groups rather than co…

math.NT2015★ 2 cited

Higher Chern classes in Iwasawa theory

F. M. Bleher, T. Chinburg, R. Greenberg +4

We begin a study of m-th Chern classes and m-th characteristic symbols for Iwasawa modules which are supported in codimension at least m. This extends the classical theory of chara…

math.NT2014

Non-commutative q-expansions

Mahesh Kakde

In this short note we partially answer a question of Fukaya and Kato by constructing a -expansion with coefficients in a non-commutative Iwasawa algebra whose constant term is a…

math.NT2013

Kato's Local epsilon conjecture: case

Mahesh Kakde

Kato and Fukaya conjectured existence of certain elements in certain (-adic) Iwasawa algebras which are related to Deligne-Langland's (-adic) local epsilon constants. We prov…

math.NT2010★ 7 cited

The main conjecture of Iwasawa theory for totally real fields

Mahesh Kakde

The purpose of this paper is to prove the main conjecture of non-commutative Iwasawa theory for p-adic Lie extensions, for an odd prime p, of totally real number fields assuming th…

math.NT2010★ 3 cited

K_1 of some Iwasawa algebras

Mahesh Kakde

Noncommutative Iwasawa theory has created a lot of interest in Whitehead groups of Iwasawa algebras of compact p-adic Lie groups with a quotient isomorphic to the additive group of…

math.NT2010★ 2 cited

K_1 of some noncommutative group rings

Mahesh Kakde

In this article I generalise previous computations (by K. Kato, T. Hara and myself) of K_1 (only up to p-power torsion) of p-adic group rings of finite non-abelian p-groups in term…

math.NT2008★ 6 cited

Proof of the Main Conjecture of Noncommutative Iwasawa Theory for Totally Real Number Fields in Certain Cases

Mahesh Kakde

Fix an odd prime . Let be a compact -adic Lie group containing a closed, normal, pro- subgroup which is abelian and such that is isomorphic to the additive g…