Junior Geometry Seminar – Calle Sönne

Abstract: Over the complex numbers, de Rham cohomology admits two filtrations. One given by holomorphic differentials, and another given by anti-holomorphic differentials. Classical Hodge theory tells us that these filtrations are “opposed” to each other, and that together they provide a decomposition of de Rham cohomology (the Hodge decomposition). In this talk, I will present an analogue of this story in characteristic p. However, in this setting, the two filtrations need no longer be opposed to each other. Measuring the difference between these two filtrations provides an interesting invariant that behaves well in families, and allows us to obtain stratifications of various moduli spaces in characteristic p (e.g. moduli spaces of abelian varieties or K3s).