Cohomologie des fibr\'es en droites sur SL3 /B en caract\'eristique positive : deux filtrations et cons\'equences

Abstract

In this thesis, I will prove the existence of two filtrations of the cohomology of line bundles on SL_3/B. The first one is a two-step filtration that exists for $H^1(\mu)$ and $H^2(\mu)$ if $\mu$ is in the Griffith region. The second one exists for all $H^i(\mu)$, which is similar to the p-filtration that has been considered by Jens Carsten Jantzen.