MS Seminar (Mathematics - String Theory)

Speaker: Jeremiah Heller (Bergische Universität Wuppertal)
Title: Atiyah-Hirzebruch spectral sequences for real varieties
Date (JST): Fri, Feb 17, 2012, 15:30 - 17:00
Place: Balcony B
Abstract: In joint work with M. Voineagu, we construct a map between the spectral sequence relating motivic cohomology and algebraic $K$-theory for real varieties and Dugger's spectral sequence (also known as the slice spectral sequence) which relates Bredon cohomology and Atiyah's real $K$-theory. We construct an intermediate "semi-topological" spectral sequence relating real morphic cohomology and real semi-topological $K$-theory. In some cases the spectral sequences constructed here allows the computation of the real semi-topological $K$-theory of some real varieties in terms of Atiyah's real $K$-theory. As another application, we give a simple alternative proof of the Lichtenbaum-Quillen conjecture over the reals which avoids the technical difficulties caused by the nonconvergence of the etale Atiyah-Hirzebruch spectral sequence for real varieties.