Local Global Principles for Galois Cohomology

Joint IAS/PU Number Theory Seminar
Topic:	Local Global Principles for Galois Cohomology
Speaker:	Julia Hartmann
Affiliation:	RWTH Aachen University; Member, School of Mathematics
Date:	Thursday, December 13
Time/Room:	4:30pm - 5:30pm/S-101

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We consider Galois cohomology groups over function fields F of curves that are defined over a complete discretely valued field.

Motivated by work of Kato and others for n=3, we show that local-global principles hold for
H^n(F, Z/mZ(n-1)) for all n>1.

In the case n=1, a local-global principle need not hold. Instead, we will see that the obstruction to a local-global principle for H^1(F,G), a Tate-Shafarevich set, can be described explicitly for many (not necessarily abelian) linear algebraic groups G.

Concrete applications of the results include central simple algebras and Albert algebras.