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Tel Aviv University
Tue 12 May 2015, 3:00pm
Algebraic Groups and Related Structures
MATH 126
Real Galois cohomology of simply connected groups
MATH 126
Tue 12 May 2015, 3:00pm-4:00pm


By the celebrated Hasse principle of Kneser, Harder and Chernousov, calculating Galois cohomology  H1(K,G) of a simply connected simple
algebraic K-group G over a number field K reduces to calculating H^1(R,G) over the field of real numbers R.  In some cases, in particular, for the split simply connected R-group G of type E_7, the first calculations of H^1(R,G) appeared only in 2013 and 2014, in preprints of Jeffrey Adams, Brian Conrad, and the speaker and Zachi Evenor. All of these calculations rely on the speaker's note of 1988.

In this talk, based on joint work with Dmitry Timashev (in progress), I will explain the method of Kac diagrams for calculating the Galois cohomology set 
H^1(R,G) for a simply connected simple algebraic R-group G. I will use groups of type E_7 as an example. No prior knowledge of Galois cohomology or of groups of type E_7 will be assumed.