# The Galois module structure of l-adic realizations of Picard 1-motives and applications

@article{Greither2010TheGM,
title={The Galois module structure of l-adic realizations of Picard 1-motives and applications},
author={Cornelius Greither and Cristian D. Popescu},
journal={arXiv: Number Theory},
year={2010}
}
• Published 5 May 2010
• Mathematics
• arXiv: Number Theory
We show that the l-adic realizations of certain Picard 1-motives associated to a G-Galois cover of smooth, projective curves defined over an algebraically closed field are G-cohomologically trivial, for all primes l. In the process, we generalize a well-known theorem of Nakajima on the Galois module structure of certain spaces of Kahler differentials associated to the top curve of the cover, assuming that the field of definition is of characteristic p. If the cover and the Picard 1-motive are…
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• Mathematics, Computer Science
• 2012
This paper deduces results on the equivariant Fitting ideal of the Tate modules of the Jacobian of the top curve, and on theEquivariants Fitting Ideal of the (dual of the) degree zero class group of theTop curve.
An Equivariant Main Conjecture in Iwasawa theory and applications
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• 2011
We construct a new class of Iwasawa modules, which are the number field analogues of the p-adic realizations of the Picard 1-motives constructed by Deligne in the 1970s and studied extensively from a
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• 2022
We use our previous work [4] on the Galois module structure of –adic realizations of Picard 1–motives to construct explicit representatives in the –adified Tate class (i.e. explicit `–adic Tate
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• 2017
In a previous paper we constructed a new class of Iwasawa modules as $\ell$--adic realizations of what we called abstract $\ell$--adic $1$--motives in the number field setting. We proved in loc. cit.
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This paper deduces results on the equivariant Fitting ideal of the Tate modules of the Jacobian of the top curve, and on theEquivariants Fitting Ideal of the (dual of the) degree zero class group of theTop curve.
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