Morava E-theory of finite general linear groups.

Monday 6th November, 2017 16:00-17:00 Maths 311B

Let F be a finite field, and consider the group G=GL_n(F) and its classifying space BG.

The cohomology H*(BG; Z/p) was computed by Quillen, provided that p is

a prime different from the characteristic of F. In chromatic homotopy theory there is also

a rich body of results about other cohomological invariants of classifying spaces of finite

groups, such as Morava E-theory, and this has a network of connections with the

algebraic geometry of formal groups. It is natural to try to apply this to the case G=GL_n(F).

An old result of Tanabe gives a description of this ring that is very elegant, but hard to

make explicit and hard to connect with other aspects of the theory. I will describe a new

approach that gives much more detailed information.

This is joint work with Sam Marsh and Sam Hutchinson.

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