Sur une $q$-déformation locale de la théorie de Hodge non-abélienne en caractéristique positive

Michel Gros (1)

1 IRMAR - Institut de Recherche Mathématique de Rennes

For $p$ a prime number and $q$ a non trivial $p$th root of 1, we present the main steps of the construction of a local $q$-deformation of the "Simpson correspondence in characteristic $p$" found by Ogus and Vologodsky in 2005. The construction is based on the Morita-equivalence between a ring of $q$-twisted differential operators and its center. We also explain the expected relations between this construction and those recently done by Bhatt and Scholze. For the sake of readability, we limit ourselves to the case of dimension 1.

Domaines: Géométrie algébrique [math.AG]

Michel Gros. Sur une $q$-déformation locale de la théorie de Hodge non-abélienne en caractéristique positive. Bhatt B.; Olsson M. p-adic Hodge Theory, Springer; Cham, pp.143-160, 2020, Springer Simons Symposium Series, 978-3-030-43843-2. ⟨hal-02311156⟩