Images directes et fonctions L en cohomologie rigide
| dc.creator | Etesse, Jean-Yves | |
| dc.date | 2008-03-11 | |
| dc.date.accessioned | 2026-07-07T12:17:33Z | |
| dc.date.available | 2026-07-07T12:17:33Z | |
| dc.description | Let $k$ be a perfect field of characteristic $p>0$, $\mathcal{V}$ a complete discrete valuation ring with residue field $k$ and field of fractions $K$ of characteristic 0, and $S$ a separated $k$-scheme of finite type. When $S$ is smooth over $k$, we partially prove here a conjecture of Berthelot about the overconvergence of the higher direct images of the structure sheaf under a proper smooth morphism $f:X\to S$; when $k$ is perfect and $\mathcal{V}$ is tamely ramified such direct images are always convergent, not only for the structure sheaf but also for (almost) every convergent $F$-isocrystals. More generally, we prove this overconvergence when $f$ is liftable over $\mathcal{V}$, or when $X$ is a relative complete intersection in some projective spaces over $S$, and taking as coefficients any overconvergent isocrystals. We then apply these results to $L$-functions with coefficients such direct images with Frobenius structure: we derive rationality or meromorphy for these $L$-functions (Dwork's conjecture), and we study their $p$-adic unit zeroes and poles (Katz's conjecture) ; and explicit case concerns the ordinary abelian schemes. A more precise presentation of results by chapters is given in the introduction. | |
| dc.identifier | https://arxiv.org/abs/0803.1580 | |
| dc.identifier | http://arxiv.org/abs/0803.1580 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/212113 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 11G, 11S40, 13B22, 13B35, 13B40, 14F20, 14F30, 14G10, 14G22, 14K, 14L05, 14L15 | |
| dc.title | Images directes et fonctions L en cohomologie rigide | |
| dc.type | text |