Hodge theory theory for non-Archimedean analytic spaces

Vendredi, 16. septembre 2022 - 14:00 - 15:00

Vladimir Berkovich (Weizmann Institute)


Let $K$ be a non-Archimedean field, whose ring of integers $K^\circ$ is isomorphic to ${\bf C}[[T]]$. Then there is a faithful functor from the category of separated schemes of finite type over $\bf C$ to the category of $K$-analytic spaces, which takes $\mathcal X$ to the generic fiber $(\widehat{\mathcal X}_{K^\circ})_\eta$ of the formal completion $\widehat{\mathcal X}_{K^\circ}$ of the scheme ${\mathcal X}_{K^\circ} = \mathcal X\otimes_{\bf C} K^\circ$ along its closed fiber. In this talk, I'll describe a Hodge theory for a class of $K$-analytic spaces, which extends the classical Hodge theory for $\mathcal X$ through the above functor and generalizes related previously known complex analytic constructions.