De Rham Cohomology in Characteristic p - Advanced Topics

De Rham Cohomology in Characteristic p - Advanced Topics

Explore advanced topics in algebraic geometry through this lecture on de Rham cohomology in characteristic p. Delve into two key areas: the stacky approach to p-adic cohomology theories and its implications for the de Rham complex, including consequences for the Hodge-to-de Rham spectral sequence in F-split and quasi-F-split smooth varieties; and the discrepancy between Steenrod operations on de Rham and Hodge cohomology, leading to examples of varieties over F_p that lift to Z_p but have non-degenerate logarithmic Hodge-to-de Rham spectral sequences. Gain insights from Harvard University's Alexander Petrov in this hour-long presentation at the Institut des Hautes Etudes Scientifiques (IHES).