Frobenius morphisms over Z/p^2 and Bott vanishing
| dc.creator | Buch, A. | |
| dc.creator | Thomsen, J. F. | |
| dc.creator | Lauritzen, N. | |
| dc.creator | Mehta, V. B. | |
| dc.date | 1995-08-17 | |
| dc.date.accessioned | 2026-07-07T09:06:37Z | |
| dc.date.available | 2026-07-07T09:06:37Z | |
| dc.description | Let $X$ be a smooth projective algebraic variety over $Z/p$, which has a flat lift to a scheme $X'$ over $Z/p^2$. If the absolute Frobenius morphism $F$ on $X$ lifts to a morphism on $X'$, then an old trick by Mazur shows that push-down of the de Rham complex under $F$ decomposes. We show that the quasi-isomorphism in question is split. This is then applied to toric varieties (where a glueing argument gives lifting of Frobenius to $Z/p^2$) and we derive natural characteristic $p$ proofs of Bott vanishing and degeneration of the Danilov spectral sequence. For flag varieties we obtain generalizations of a result of Paranjape and Srinivas about non-lifting of Frobenius to the Witt vectors. | |
| dc.description | AMS-LaTeX, For a dvi-version of this preprint please check out http://www.mi.aau.dk/~niels/papers.html | |
| dc.identifier | https://arxiv.org/abs/alg-geom/9508009 | |
| dc.identifier | http://arxiv.org/abs/alg-geom/9508009 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/150071 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 14F17 (Primary) 14M25, 14M15 (Secondary) | |
| dc.title | Frobenius morphisms over Z/p^2 and Bott vanishing | |
| dc.type | text |