On the {\'e}tale cohomology of algebraic varieties with totally degenerate reduction over p-adic fields
Vol. 14 (2007), No. 2, Page 261--291.
Raskind, Wayne ; Xarles, Xavier
On the {\'e}tale cohomology of algebraic varieties with totally degenerate reduction over p-adic fields
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Abstract:
Let K be a field of characteristic zero that is complete with respect to a discrete valuation, with perfect residue field of characteristic p>0. We formulate the notion of {\it totally degenerate reduction} for a smooth projective variety X over K. We show that for all prime numbers ℓ, the \bQl-\'etale cohomology of such a variety is (after passing to a suitable finite unramified extension of K) a successive extension of direct sums of Galois modules of the form \bQl(r). More precisely, this cohomology has an increasing filtration whose r-th graded quotient is of the form V⊗\bQ\bQl(r), where V is a finite dimensional \bQ-vector space that is independent of ℓ, with an unramified action of the absolute Galois group of K.
Mathematics Subject Classification (2000): Primary 14F20, 14F30 , Secondary 14G20
Mathematical Reviews Number: MR2351367
Received: 2004-12-24
