Course and Project Description: The rank one abelian Stark conjecture
نویسندگان
چکیده
Let K/F denote an abelian extension of number fields with associated rings of integers OK and OF . Let S denote a finite set of places of F containing the archimedean places and those which ramify in K. Assume that S contains at least one place v that splits completely in K and that |S| ≥ 2. For each ideal n ⊂ OF not divisible by a prime that ramifies in K, we denote by σn the associated Frobenius element in Gal(K/F ). For each element σ ∈ G := Gal(K/F ), we define the partial zeta-function
منابع مشابه
Index formulae for Stark units and their solutions
Let K/k be an abelian extension of number fields with a distinguished place of k that splits totally in K. In that situation, the abelian rank one Stark conjecture predicts the existence of a unit in K, called the Stark unit, constructed from the values of the L-functions attached to the extension. In this paper, assuming the Stark unit exists, we prove index formulae for it. In a second part, ...
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A refinement of the rank 1 abelian Stark conjecture has been formulated by B. Gross. This conjecture predicts some p-adic analytic nature of a modification of the Stark unit. The conjecture makes perfect sense even when p is an archimedean place. Here we consider the conjecture when p is a real place, and interpret it in terms of 2-adic properties of special values of L-functions. We prove the ...
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