Marian Anton
Central Connecticut State University, New Britain, USA & Simion Stoilow Institute of Mathematics of the Romanian Academy, Bucharest, Romania

The integral cohomology of $GL_n$ and its stable version $GL$ over a ring of integers $\mathcal O_F$ in a number field $F$ has been the source of rich mathematical ideas. One approach is to localize the problem at each prime $p$. In this talk, we look at mod $p$ cohomology of $GL_n\mathcal O_F[1/p]$ where $F$ is the cyclotomic field of $p$-roots of unity. In particular, we describe some explicit cycles in the mod $p$ homology of $SL_2\mathcal O_F[1/p]$ which are relevant for the general case.