7 citations · 31 across the 18 of their papers we have counts for
19 papers · 1 filter
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…
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…
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…
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 .
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…