On Iwasawa theory, zeta elements for 𝔾m, and the equivariant Tamagawa number conjecture
نویسندگان
چکیده
منابع مشابه
Integrality of Stickelberger elements and the equivariant Tamagawa number conjecture
Let L/K be a nite Galois CM-extension of number elds with Galois group G. In an earlier paper, the author has de ned a module SKu(L/K) over the center of the group ring ZG which coincides with the Sinnott-Kurihara ideal if G is abelian and, in particular, contains many Stickelberger elements. It was shown that a certain conjecture on the integrality of SKu(L/K) implies the minus part of the equ...
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Spencer Bloch and the author formulated a general conjecture (Tamagawa number conjecture) on the relation between values of zeta functions of motives and arithmetic groups associated to motives. We discuss this conjecture, and describe some application of the philosophy of the conjecture to the study of elliptic curves. 2000 Mathematics Subject Classification: 11G40.
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We give a survey of the equivariant Tamagawa number (a.k.a. Bloch-Kato) conjecture with particular emphasis on proven cases. The only new result is a proof of the 2-primary part of this conjecture for Tate-motives over abelian fields. This article is an expanded version of a survey talk given at the conference on Stark’s conjecture, Johns Hopkins University, Baltimore, August 5-9, 2002. We have...
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The “main conjecture” of equivariant Iwasawa theory concerns the situation where • l is a fixed odd prime number and K/k is a Galois extension of totally real number fields with k/Q and K/k∞ finite, where k∞/k is the cyclotomic Zl-extension (we set G = G(K/k) and Γk = G(k∞/k)), • S is a fixed finite set (which will normally be suppressed in the notation) of primes of k containing all primes whi...
متن کاملOn the “main Conjecture” of Equivariant Iwasawa Theory
The “main conjecture” of equivariant Iwasawa theory concerns the situation where • l is a fixed odd prime number and K/k is a Galois extension of totally real number fields with k/Q and K/k∞ finite, where k∞/k is the cyclotomic Zl-extension (we set G = G(K/k) and Γk = G(k∞/k)), • S is a fixed finite set (which will normally be suppressed in the notation) of primes of k containing all primes whi...
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ژورنال
عنوان ژورنال: Algebra & Number Theory
سال: 2017
ISSN: 1944-7833,1937-0652
DOI: 10.2140/ant.2017.11.1527