http://swrc.ontoware.org/ontology#UnrefereedArticle
On the {\'e}tale cohomology of algebraic varieties with totally
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Raskind Wayne
Xarles Xavier
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 $\ell$, 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 $V\otimes_{\bQ}\bQl(r)$, where $V$ is a finite dimensional $\bQ$-vector space that is independent of $\ell$, with an unramified action of the absolute Galois group of $K$.
Journal of mathematical sciences, the University of Tokyo
14
2
261-291
2007-08-27
13405705
AA11021653
application/pdf
415
Graduate School of Mathematical Sciences, The University of Tokyo