Hodge cohomology of invertible sheaves
Abstract
v2: We improved a little bit according to the referee's wishes. v1: On $X$ projective smooth over a field $k$, Pink and Roessler conjecture that the dimension of the Hodge cohomology of an invertible $n$torsion sheaf $L$ is the same as the one of its $a$th power $L^a$ if $a$ is prime to $n$, under the assumptions that $X$ lifts to $W_2(k)$ and $dim X\le p$, if $k$ has characteristic $p>0$. They show this if $k$ has characteristic 0 and if $n$ is prime to $p$ in characteristic $p>0$. We show the conjecture in characteristic $p>0$ if $n=p$ assuming in addition that $X$ is ordinary (in the sense of BlochKato).
 Publication:

arXiv eprints
 Pub Date:
 September 2007
 arXiv:
 arXiv:0709.3447
 Bibcode:
 2007arXiv0709.3447E
 Keywords:

 Mathematics  Algebraic Geometry
 EPrint:
 13 pages