Real Galois cohomology of simply connected groups

Seminar
Speaker
Prof. Mikhail Borovoi (Tel Aviv University)
Date
11/03/2015 - 11:15 - 10:15Add to Calendar 2015-03-11 10:15:00 2015-03-11 11:15:00 Real Galois cohomology of simply connected groups By the celebrated Hasse principle of Kneser, Harder and Chernousov, calculating the Galois cohomology  H^1(K,G)  of a simply connected simple K-group over a number field K reduces to calculating H^1(R,G) over the field of real numbers R.  For 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 Jeffry Adams, of Brian Conrad, and of the speaker and Zachi Evenor. All these calculations used the speaker's note of 1988. In the talk I will explain the method of Kac diagrams of calculating H^1(R,G)  for a simply connected simple R-group G by the examples of groups of type E_7. The talk is based on a work in progress with Dmitry A. Timashev. No preliminary knowledge of Galois cohomology or of groups of type E_7 is assumed. Third floor seminar room אוניברסיטת בר-אילן - Department of Mathematics mathoffice@math.biu.ac.il Asia/Jerusalem public
Place
Third floor seminar room
Abstract

By the celebrated Hasse principle of Kneser, Harder and Chernousov,
calculating the Galois cohomology  H^1(K,G)  of a simply connected simple
K-group over a number field K reduces to calculating H^1(R,G) over the
field of real numbers R.  For 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 Jeffry Adams,
of Brian Conrad, and of the speaker and Zachi Evenor. All these
calculations used the speaker's note of 1988.

In the talk I will explain the method of Kac diagrams of calculating
H^1(R,G)  for a simply connected simple R-group G by the examples of
groups of type E_7. The talk is based on a work in progress with
Dmitry A. Timashev. No preliminary knowledge of Galois cohomology or
of groups of type E_7 is assumed.

Last Updated Date : 04/03/2015