MATH Seminar

Title: Field Patching and Galois Cohomology -- Indecomposable and Noncrossed Product Division Algebras over Curves
Defense: Dissertation
Speaker: Feng Chen of Emory University
Contact: Feng Chen, fchen@emory.edu
Date: 2010-07-09 at 4:00PM
Venue: MSC W301
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Abstract: Let $T$ be a complete discrete valuation ring and let $\hat X$ be a smooth projective $T$-curve. In this talk I will talk about construction of indecomposable and noncrossed product division algebras over $F$, which is the function field of $\hat X$.\\ \\ The construction is based on the technique "patching over fields", which was proposed by Harbater and Hartmann. In this talk I will recall the technique and present its application to Galois cohomology. In particular, I will apply this patching technique to construct an index preserving section ${\mathrm Br}(\hat F)\to{\mathrm Br}(F)$ (where $\hat F$ is the completion of $F$ with respect to the valuation induced by the closed fibre), which splits the restriction and use this section to lift indecomposable and noncrossed product division algebras over $\hat F$ to $F$.