On the Hodge to de Rham spectral sequence in positive characteristic, after A. Petrov
On the Hodge to de Rham spectral sequence in positive characteristic, after A. Petrov

Luc Illusie, University of Paris
Fine Hall 322
Let $k$ be a perfect field of characteristic $p>0$. A. Petrov has recently constructed a projective, smooth scheme $X/W(k)$, of relative dimension $p+1$, such that the Hodge to de Rham spectral sequence of $X_0/k$, where $X_0 = X \otimes_{W(k}k$, does not degenerate at $E_1$, thus solving a question of DeligneIllusie left open since 1987. I will explain the main ideas of the proof, which uses inputs from BhattLurie's theory of diffracted Hodge complexes and combines techniques of homotopical algebra and representation theory of algebraic groups.