Numerical Evidence Toward a 2-adic Equivariant “Main Conjecture”
نویسندگان
چکیده
منابع مشابه
Numerical Evidence Toward a 2-adic Equivariant "Main Conjecture"
1. The conjecture Let K be a totally real finite Galois extension of Q with Galois group G dihedral of order 8, and suppose that √ 2 is not in K. Fix a finite set S of primes of Q including 2, ∞ and all primes that ramify in K. Let C be the cyclic subgroup of G of order 4 and F the fixed field of C acting on K. Fix a 2-adic unit u ≡ 5 mod 8Z 2. Write L F (s, χ) for the 2-adic L-functions, norma...
متن کاملNumerical Evidence for the Equivariant Birch and Swinnerton-Dyer Conjecture
In the first part of the talk we describe an algorithm which computes a relative algebraic K-group as an abstract abelian group. We also show how this representation can be used to do computations in these groups. This is joint work with Steve Wilson. Our motivation for this project originates from the study of the Equivariant Tamagawa Number Conjecture which is formulated as an equality of an ...
متن کامل`-adic Modular Deformations and Wiles’s “main Conjecture”
Let E be an elliptic curve over Q. The Shimura-Taniyama conjecture asserts that E is modular, i.e., that there is a weight-two newform f such that ap(f) = ap(E) for all primes p at which E has good reduction. Let ` be a prime, choose a basis for the Tate module T`(E) and consider the `-adic representation ρE,` : GQ → Aut(T`(E)) ∼= GL2(Z`). Then E is modular if and only if ρE,` is modular, i.e.,...
متن کاملEquivariant Bloch-Kato conjecture and non-abelian Iwasawa Main Conjecture
In this talk we explain the relation between the (equivariant) Bloch-Kato conjecture for special values of L-functions 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 non-abelian case would allow to reduce the general conjecture to the case of number fields...
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...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Experimental Mathematics
سال: 2011
ISSN: 1058-6458,1944-950X
DOI: 10.1080/10586458.2011.564541