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On the etale cohomology of algebraic varieties with totally degenerate reduction over p-adic fields

Wayne Raskind·Xavier Xarles
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Abstract

Let K be a finite extension of Q_p and X a smooth projective variety over K. We define the notion of totally degenerate reduction of such an X and the associated Chow complexes of the special fibre of a suitable regular proper model of X over the ring of integers of K. If X has such reduction, we then show that for all l, the Q_l-adic etale cohomology of X has a filtration whose graded quotients are isomorphic, as Galois modules, to the tensor product of a finite dimensional Q-vector space (with a finite unramified action of Galois) with twists of Q_l by the cyclotomic character.

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Wayne Raskind, Xavier Xarles. 2006-01-25. On the etale cohomology of algebraic varieties with totally degenerate reduction over p-adic fields. https://arxiv.org/abs/math/0306123

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