Discrete invariants of varieties in positive characteristic
| dc.creator | Moonen, B. | |
| dc.creator | Wedhorn, T. | |
| dc.date | 2003-06-24 | |
| dc.date | 2004-04-16 | |
| dc.date.accessioned | 2026-07-07T04:59:08Z | |
| dc.date.available | 2026-07-07T04:59:08Z | |
| dc.description | If $S$ is a scheme of characteristic $p$, we define an $F$-zip over $S$ to be a vector bundle with two filtrations plus a collection of semi-linear isomorphisms between the graded pieces of the filtrations. For every smooth proper morphism $X\to S$ satisfying certain conditions the de Rham bundles $H^n_{\rm dR}(X/S)$ have a natural structure of an $F$-zip. We give a complete classification of $F$-zips over an algebraically closed field by studying a semi-linear variant of a variety that appears in recent work of Lusztig. For every $F$-zip over $S$ our methods give a scheme-theoretic stratification of $S$. If the $F$-zip is associated to an abelian scheme over $S$ the underlying topological stratification is the Ekedahl-Oort stratification. We conclude the paper with a discussion of several examples such as good reductions of Shimura varieties of PEL type and K3-surfaces. | |
| dc.description | 35 pages, minor changes in exposition, major changes to introduction | |
| dc.identifier | https://arxiv.org/abs/math/0306339 | |
| dc.identifier | http://arxiv.org/abs/math/0306339 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/67862 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Number Theory | |
| dc.subject | 14J10, 14F40 (Primary) 14J28, 11G18, 14K10, 20G40 (Secondary) | |
| dc.title | Discrete invariants of varieties in positive characteristic | |
| dc.type | text |