Results 1  10
of
12
Tamagawa Numbers for Motives with (NonCommutative) Coefficients
 DOCUMENTA MATH.
, 2001
"... Let M be a motive which is defined over a number field and admits an action of a finite dimensional semisimple Qalgebra A. We formulate and study a conjecture for the leading coefficient of the Taylor expansion at 0 of the Aequivariant Lfunction of M. This conjecture simultaneously generalizes a ..."
Abstract

Cited by 37 (11 self)
 Add to MetaCart
Let M be a motive which is defined over a number field and admits an action of a finite dimensional semisimple Qalgebra A. We formulate and study a conjecture for the leading coefficient of the Taylor expansion at 0 of the Aequivariant Lfunction of M. This conjecture simultaneously generalizes and refines the Tamagawa number conjecture of Bloch, Kato, Fontaine, PerrinRiou et al. and also the central conjectures of classical Galois module theory as developed by Fröhlich, Chinburg, M. Taylor et al. The precise formulation of our conjecture depends upon the choice of an order A in A for which there exists a ‘projective Astructure ’ on M. The existence of such a structure is guaranteed if A is a maximal order, and also occurs in many natural examples where A is nonmaximal. In each such case the conjecture with respect to a nonmaximal order refines the conjecture with respect to a maximal order. We develop a theory of determinant functors for all orders in A by making use of the category of virtual objects introduced by Deligne.
On the Equivariant Tamagawa Number Conjecture for Tate Motives, Part II
 DOCUMENTA MATH.
, 2006
"... Let K be any finite abelian extension of Q, k any subfield of K and r any integer. We complete the proof of the equivariant Tamagawa Number Conjecture for the pair (h0(Spec(K))(r), Z[Gal(K/k)]). ..."
Abstract

Cited by 29 (7 self)
 Add to MetaCart
Let K be any finite abelian extension of Q, k any subfield of K and r any integer. We complete the proof of the equivariant Tamagawa Number Conjecture for the pair (h0(Spec(K))(r), Z[Gal(K/k)]).
Adjoint motives of modular forms and the Tamagawa number conjecture
, 2001
"... This paper concerns the Tamagawa number conjecture of Bloch and Kato [BK] for adjoint motives of modular forms of weight k ≥ 2. The conjecture relates the value at 0 of the associated Lfunction to arithmetic invariants of the motive. We prove that it holds up to powers of certain “bad primes. ” Th ..."
Abstract

Cited by 10 (2 self)
 Add to MetaCart
This paper concerns the Tamagawa number conjecture of Bloch and Kato [BK] for adjoint motives of modular forms of weight k ≥ 2. The conjecture relates the value at 0 of the associated Lfunction to arithmetic invariants of the motive. We prove that it holds up to powers of certain “bad primes. ” The strategy for achieving
Equivariant BlochKato conjecture and nonabelian Iwasawa main conjecture
 in Proceedings of the International Congress of Mathematicians, Vol. II (Beijing, 2002), 149–162, Higher Ed
"... In this talk we explain the relation between the (equivariant) BlochKato conjecture for special values of Lfunctions and the Main Conjecture of (nonabelian) Iwasawa theory. On the way we will discuss briefly the case of Dirichlet characters in the abelian case. We will also discuss how “twisting ” ..."
Abstract

Cited by 9 (0 self)
 Add to MetaCart
In this talk we explain the relation between the (equivariant) BlochKato conjecture for special values of Lfunctions and the Main Conjecture of (nonabelian) Iwasawa theory. On the way we will discuss briefly the case of Dirichlet characters in the abelian case. We will also discuss how “twisting ” in the nonabelian case would allow to reduce the general conjecture to the case of number fields. This is one the main motivations for a nonabelian Main
On the Equivariant Tamagawa Number Conjecture for Abelian Extensions of a Quadratic Imaginary Field
 DOCUMENTA MATH.
, 2006
"... Let k be a quadratic imaginary field, p a prime which splits in k/Q and does not divide the class number hk of k. Let L denote a finite abelian extension of k and let K be a subextension of L/k. In this article we prove the ppart of the Equivariant Tamagawa Number Conjecture for the pair (h 0 (Spe ..."
Abstract

Cited by 7 (0 self)
 Add to MetaCart
Let k be a quadratic imaginary field, p a prime which splits in k/Q and does not divide the class number hk of k. Let L denote a finite abelian extension of k and let K be a subextension of L/k. In this article we prove the ppart of the Equivariant Tamagawa Number Conjecture for the pair (h 0 (Spec(L)), Z[Gal(L/K)]).
Symmetric Square LFunctions and ShafarevichTate Groups.” Experiment
 Math
"... We use Zagier's method to compute the critical values of the 1. Introduction symmetric square Lfunctions of six cuspidal eigenforms of level 2. Calculating the Critical Values one with rational coefficients. According to the BlochKato 3. Tables of Results conjecture, certain large primes dividing ..."
Abstract

Cited by 4 (2 self)
 Add to MetaCart
We use Zagier's method to compute the critical values of the 1. Introduction symmetric square Lfunctions of six cuspidal eigenforms of level 2. Calculating the Critical Values one with rational coefficients. According to the BlochKato 3. Tables of Results conjecture, certain large primes dividing these critical values
A Bound for the Torsion in the KTheory of Algebraic Integers
 DOCUMENTA MATH.
, 2003
"... Let m be an integer bigger than one, A a ring of algebraic integers, F its fraction field, and Km(A) the mth Quillen Kgroup of A. We give a (huge) explicit bound for the order of the torsion subgroup of Km(A) (up to small primes), in terms of m, the degree of F over Q, and its absolute discrimin ..."
Abstract

Cited by 3 (0 self)
 Add to MetaCart
Let m be an integer bigger than one, A a ring of algebraic integers, F its fraction field, and Km(A) the mth Quillen Kgroup of A. We give a (huge) explicit bound for the order of the torsion subgroup of Km(A) (up to small primes), in terms of m, the degree of F over Q, and its absolute discriminant.
GENERATORS AND RELATIONS FOR K2OF
"... Abstract. Tate’s algorithm for computing K2OF for rings of integers in a number field has been adapted for the computer and gives explicit generators for the group and sharp bounds on their order—the latter, together with some structural results on the pprimary part of K2OF due to Tate and Keune, g ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
Abstract. Tate’s algorithm for computing K2OF for rings of integers in a number field has been adapted for the computer and gives explicit generators for the group and sharp bounds on their order—the latter, together with some structural results on the pprimary part of K2OF due to Tate and Keune, gives a proof of its structure for many number fields of small discriminants, confirming earlier conjectural results. For the first time, tame kernels of non
ON THE EQUIVARIANT MAIN CONJECTURE OF IWASAWA THEORY
, 2005
"... The main conjecture of Iwasawa theory for an abelian number field in its classical formulation describes the Galoismodule structure of the class groups in the limit over the intermediate fields of its cyclotomic Zpextension. The eigenspace of this limit with respect to a Dirichlet ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
The main conjecture of Iwasawa theory for an abelian number field in its classical formulation describes the Galoismodule structure of the class groups in the limit over the intermediate fields of its cyclotomic Zpextension. The eigenspace of this limit with respect to a Dirichlet
Generators and Relations for ... Imaginary Quadratic
"... Tate's algorithm [31] for computing K 2 OF for rings of integers in a number field has been adapted for the computer and gives explicit generators for the group and sharp bounds on their order  the latter, together with some structural results on the pth primary part of K 2 OF due to Tate and Keun ..."
Abstract
 Add to MetaCart
Tate's algorithm [31] for computing K 2 OF for rings of integers in a number field has been adapted for the computer and gives explicit generators for the group and sharp bounds on their order  the latter, together with some structural results on the pth primary part of K 2 OF due to Tate and Keune, gives a proof of its structure for many imaginary quadratic fields, confirming earlier conjectural results in [7].