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 タイトル: On the {\'e}tale cohomology of algebraic varieties with totally 著者: Raskind, WayneXarles, Xavier 発行日: 2007年8月27日 出版者: Graduate School of Mathematical Sciences, The University of Tokyo 掲載誌情報: Journal of Mathematical Sciences, The University of Tokyo. Vol. 14 (2007), No. 2, Page 261-291 抄録: 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 $K$. URI: http://hdl.handle.net/2261/15755 ISSN: 13405705 出現カテゴリ: Journal of Mathematical Sciences, the University of TokyoJournal of Mathematical Sciences, the University of Tokyo

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