Tori over a p-adic function field
Vortrag von Prof. Dr. Tamás Szamuely
Sprecher eingeladen von: Prof. Dr. Joseph Ayoub
Datum: 28.10.13 Zeit: 13.15 - 14.45 Raum: Y27H25
I shall report on joint work with David Harari concerning local-global questions for Galois cohomology over the function field of a curve defined over a p-adic field. We consider analogues of the Tate-Shafarevich group in this situation and prove that they satisfy a duality theorem. As an application, we show that the failure of the local-global principle for rational points on principal homogeneous spaces under tori is controlled by a certain subquotient of a third etale cohomology group.If time permits, I shall also explain a generalization to principal homogeneous spaces of certain reductive group schemes in the case when the base curve has good reduction.