A&NT seminar: Oli Gregory

Speaker: Oli Gregory (Technische Universität München)

Title: Around p-adic Tate conjectures

Abstract: I shall explore Tate conjectures for smooth and proper varieties over p-adic fields, especially a conjecture of Raskind which concerns varieties with totally degenerate reduction. After first motivating the conjecture and discussing some evidence, I shall reformulate Raskind's conjecture into a subtle question about Q- versus Q_p-structures on filtered (phi,N)-modules. I will then use this reformulation to show that Raskind's conjecture can fail even for abelian surfaces. This is joint work with Christian Liedtke.