2020-08-08T12:15:08Zhttps://repository.dl.itc.u-tokyo.ac.jp/?action=repository_oaipmhoai:repository.dl.itc.u-tokyo.ac.jp:000401072020-07-10T06:57:17Z00312:06865:06949:0695500009:00504:06868:06951:06956
On the {\'e}tale cohomology of algebraic varieties with totallyenghttp://hdl.handle.net/2261/15755Departmental Bulletin PaperRaskind, WayneXarles, XavierLet $K$ 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 Tokyo1422612912007-08-2713405705AA11021653application/pdf415https://repository.dl.itc.u-tokyo.ac.jp/?action=repository_action_common_download&item_id=40107&item_no=1&attribute_id=19&file_no=1Graduate School of Mathematical Sciences, The University of Tokyo2017-06-14