Morava E-theory of finite general linear groups.
Neil Strickland (Sheffield)
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.