**Title:** A Tate duality theorem for local Galois symbols

**Speaker:** Evangelia Gazaki

**Speaker Info:** University of Michigan

**Brief Description:**

**Special Note**:

**Abstract:**

Let K be a p-adic field and M a finite continuous Gal(\bar K/K)-module. Local Tate duality is a perfect duality between the Galois cohomology of M and the Galois cohomology of its dual module. In the special case when M is the module of the m-torsion points of an abelian variety A over K, Tate has a finer result.In this case the group H^1(K,M) has a "significant subgroup", namely there is a map A(K)/m -> H^1 (K,M) induced by the Kummer sequence on A. Tate showed that under the perfect pairing for H^1, the orthogonal complement of A(K)/m is the corresponding part, A^*(K)/m, where A^* is the dual abelian variety of A.In this talk I will present an analogue of this classical result for H^2. The "significant subgroup" in this case will be given by a Galois symbol map, similar to the classical Galois symbol of the motivic Bloch-Kato conjecture, while the orthogonal complement under the Tate duality pairing will be given by an object of p-adic Hodge theory.

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