Dienstag/Donnerstag: 10:00-12:00. HS :B 046.

This Lecture is a sequel to ``Trees and Homology of SL2 (I)" given in Wintersemester 2013/14. Our aim is to study the homology of SL_2 over polynomial rings and to apply these results to get information on the homology of SL_2(F), F an algebraically closed field. We will start with a further study the tree of SL_2 over field with a discrete valuation, in particular we will give the geometric interpretation in terms of rank 2 vector bundles over curves. We will then define the tree of SL_2 over a polynomial rings and give the generalization of the geometric interpretation in that case using germs of rank 2 vector bundles over projective spaces. We then collect informations on the the homology of SL_2 over a polynomial rings by studying the action of that group on this tree. At the end we will sketch a proof of the weak homotopy invariant property for SL_2, one of the key step in the proof of the Friedlander-Milnor conjecture computing the homology of SL_2(F) with F an algebraically closed field.

References:

J.-P. Serre, Trees, Springer.

R. Hartschorne, Algebraic geometry, Springer.

P.J. Hilton, U. Stammbach, A course in homological algebra, Springer.