On derivatives of p-adic L-series at s = 0
TLDR
In this paper, the authors used non-commutative Iwasawa theory to investigate the values at zero of higher derivatives of the p-adic Artin L-series.Abstract:
Abstract We use techniques of non-commutative Iwasawa theory to investigate the values at zero of higher derivatives of p-adic Artin L-series.read more
Citations
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Journal ArticleDOI
A first course in noncommutative rings, by T. Y. Lam. Pp. 385. £37 (pb), £62.50 (hb). 2001. ISBN 0 387 95325 6 (pb), 0 387 95183 0 (hb) (Springer-Verlag).
TL;DR: In this paper, a text on rings, fields and algebras is intended for graduate students in mathematics, aiming the level of writing at the novice rather than at the expert, and by stressing the role of examples and motivation.
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An unconditional proof of the abelian equivariant Iwasawa main conjecture and applications
Henri Johnston,Andreas Nickel +1 more
TL;DR: In this article, the authors give an unconditional proof of the equivariant Iwasawa main conjecture for totally real fields for every admissible one-dimensional $p$-adic Lie extension whose Galois group has an abelian Sylow subgroup.
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On the Brumer-Stark Conjecture
Samit Dasgupta,Mahesh Kakde +1 more
TL;DR: In this paper, a stronger version of the Brumer-stark conjecture was conjectured by Kurihara that gives a formula for the 0th Fitting ideal of the minus part of the Pontryagin dual of a group ring valued Hilbert modular form in terms of Stickelberger elements.
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Notes on the dual of the ideal class groups of CM-fields
TL;DR: In this paper, for a CM abelian extension of number fields, a conjecture which describes completely the Fitting ideal of the minus part of the Pontryagin dual of the $T$-ray class group of $K$ for a set of primes as a ${\rm Gal}(K/k)$-module was proposed.
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On the non-abelian Brumer-Stark conjecture and the equivariant Iwasawa main conjecture
Henri Johnston,Andreas Nickel +1 more
TL;DR: In this paper, it was shown that for an odd prime p, the p-primary parts of refinements of the non-abelian Brumer and Brumer-Stark conjectures are implied by the equivariant Iwasawa main conjecture (EIMC) for real fields.
References
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Book
Cohomology of Groups
TL;DR: In this paper, an advanced textbook introduces students to cohomology theory and no knowledge of homological algebra is assumed beyond what is normally taught in a first course in algebraic topology.
Journal ArticleDOI
A first course in noncommutative rings, by T. Y. Lam. Pp. 385. £37 (pb), £62.50 (hb). 2001. ISBN 0 387 95325 6 (pb), 0 387 95183 0 (hb) (Springer-Verlag).
TL;DR: In this paper, a text on rings, fields and algebras is intended for graduate students in mathematics, aiming the level of writing at the novice rather than at the expert, and by stressing the role of examples and motivation.
Book
A first course in noncommutative rings
TL;DR: In this article, a text on rings, fields and algebras is intended for graduate students in mathematics, aiming the level of writing at the novice rather than at the expert, and by stressing the role of examples and motivation.
Book ChapterDOI
Société Mathématique de France
TL;DR: In this article, a formal theory of Tannaka duality inspired by Ross Street's "formal theory of monads" is presented. But the formal theory is restricted to the case where the representations of the representations are over an arbitrary commutative ring rather than a field.
Journal ArticleDOI
The Iwasawa conjecture for totally real fields
TL;DR: In this paper, it was shown that a p-adic L-function associated to a one-dimensional Artin character 4 with F is continuous for s e Zp{ 1, and even at s = 1 if 4, is not trivial.