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20
BlochKato conjecture and Main Conjecture of Iwasawa theory for Dirichlet characters
, 2002
"... The Tamagawa number conjecture proposed by S. Bloch and K. Kato describes the “special values ” of Lfunctions in terms of cohomological data. The main conjecture of Iwasawa theory describes a padic Lfunction in terms of the structure of modules for the Iwasawa algebra. We give a complete proof of ..."
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Cited by 14 (2 self)
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The Tamagawa number conjecture proposed by S. Bloch and K. Kato describes the “special values ” of Lfunctions in terms of cohomological data. The main conjecture of Iwasawa theory describes a padic Lfunction in terms of the structure of modules for the Iwasawa algebra. We give a complete proof of both conjectures (up to the prime 2) for Lfunctions attached to Dirichlet characters. We use the insight of Kato and B. PerrinRiou that these two conjectures can be seen as incarnations of the same mathematical content. In particular, they imply each other. By a bootstrapping process using the theory of Euler systems and explicit reciprocity laws, both conjectures are reduced to the analytic class number formula. Technical problems with primes dividing the order of the character are avoided by using the correct cohomological formulation of the main conjecture.
Degeneration of ladic Eisenstein classes and of the elliptic polylog
"... 1.1 A residue sequence in Ktheory................. 7 1.2 The Eisenstein symbol...................... 8 ..."
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Cited by 13 (6 self)
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1.1 A residue sequence in Ktheory................. 7 1.2 The Eisenstein symbol...................... 8
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 ” ..."
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Cited by 9 (0 self)
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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
Dirichlet motives via modular curves
, 1997
"... Generalizing ideas of Anderson, Harder has proposed a construction of extensions of motives of DirichletTate type in sheaf theoretic terms (cf. [Ha] Section 4.2 or the review before Prop. 6.4). Let Mk(−1) be the smooth l ..."
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Cited by 3 (3 self)
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Generalizing ideas of Anderson, Harder has proposed a construction of extensions of motives of DirichletTate type in sheaf theoretic terms (cf. [Ha] Section 4.2 or the review before Prop. 6.4). Let Mk(−1) be the smooth l
Filtrations On Higher Algebraic KTheory
 In Algebraic Ktheory
, 1983
"... this paper is to compare the analogous ltrations for the higher ..."
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Cited by 2 (1 self)
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this paper is to compare the analogous ltrations for the higher
On the generalized Eisenstein symbol
, 1997
"... According to the Beilinson conjectures, there is an intimate connection between the Ktheory, or motivic cohomology, of a smooth proper variety X over Q, and special values of the Lfunction of X: The latter are expected to compare two Qstructures on the highest exterior power of the Deligne ..."
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Cited by 1 (0 self)
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According to the Beilinson conjectures, there is an intimate connection between the Ktheory, or motivic cohomology, of a smooth proper variety X over Q, and special values of the Lfunction of X: The latter are expected to compare two Qstructures on the highest exterior power of the Deligne
Specialization of the padic Polylogarithm to pth Power Roots of Unity
 DOCUMENTA MATH.
, 2003
"... The purpose of this paper is to calculate the restriction of the padic polylogarithm sheaf to pth power torsion points. ..."
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Cited by 1 (1 self)
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The purpose of this paper is to calculate the restriction of the padic polylogarithm sheaf to pth power torsion points.
ON UNIQUENESS OF CHARACTERISTIC CLASSES
, 2006
"... Abstract. We give tools to compare different maps from algebraic Ktheory. The results apply in particular to group morphisms from Ktheory to any suitable cohomology theory or to Ktheory. In particular, we obtain a characterization of the Chern character and of the Adams operations on higher Kthe ..."
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Cited by 1 (1 self)
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Abstract. We give tools to compare different maps from algebraic Ktheory. The results apply in particular to group morphisms from Ktheory to any suitable cohomology theory or to Ktheory. In particular, we obtain a characterization of the Chern character and of the Adams operations on higher Ktheory.