Cornelius Greither

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We apply an equivariant version of the p-adic Weierstrass Preparation Theorem in the context of possible non-commutative generalizations of the power series of Deligne and Ribet. We then consider CM abelian extensions of totally real fields and by combining our earlier considerations with the known validity of the Main Conjecture of Iwasawa theory we prove,(More)
In this paper, we systematically construct abelian extensions of CM-fields over a totally real field whose Stickelberger elements are not in the Fitting ideals of the class groups. Our evidence indicates that Pontryagin duals of class groups behave better than the class groups themselves. We also explore the behaviour of Fitting ideals under projective(More)
Let Z −→ Z be a G–Galois cover of smooth, projective curves over an arbitrary algebraically closed field κ, and let S and T be G–equivariant, disjoint, finite, non-empty sets of closed points on Z, such that S contains the ramification locus of the cover. In this context, we prove that the l–adic realizations Tl(MS,T ) of the Picard 1–motive MS,T associated(More)
As a starting point, an important link is established between Brumer’s conjecture and the Brumer-Stark conjecture which allows one to translate recent progress on the former into new results on the latter. For example, if K/F is an abelian extension of relative degree 2p, p an odd prime, we prove the l-part of the Brumer-Stark conjecture for all odd primes(More)
In previous work, we proved a result on the equivariant Fitting ideal of the `-adic realization of the Picard 1-motive attached to an abelian covering of curves defined over a finite field. In this paper, we build upon this work to deduce results on the equivariant Fitting ideal of the Tate modules of the Jacobian of the top curve, and on the equivariant(More)
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