2
$\begingroup$

For a smooth hypersurface $X\subset\mathbb{P}^n_k$, where $k$ is an algebraic closed field of charactersitc $p>0$. How to compute its algebraic de Rham cohomology explicitly? or equivalently its Hodge number?

PS：In characteristic $0$ case, one has Lefschetz hyperplane theorem,Hirzebruch-Riemann-Roch and Hodge theory.

Improve this question
$\endgroup$
1
  • 5
    $\begingroup$ The same formulas as in characteristic $0$ hold in characteristic $p> 0$. See the exposition by Deligne in SGA 7 II, Expose XI. $\endgroup$
    – naf
    Commented Feb 22, 2012 at 14:33

0

Reset to default

You must log in to answer this question.

Browse other questions tagged .