WSU

Department of Mathematics
Topology Seminar 2006-2007

Wayne State University
College of Science


All talks are held Tuesdays at 2:00 PM in 1285 FAB, unless otherwise noted.
Contact Dan Isaksen (isaksen AT math.wayne.edu) for more information

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Date: February 12, 2008

Speaker:  Dan Isaksen, Wayne State University

Title: Motivic homological algebra

Abstract: 

I will describe some preliminary explicit computations in motivic homotopy theory.  Over arbitrary ground fields, we just don't know enough to compute much.  But over the complex numbers, we have explicit descriptions (due to Voevodsky) of the cohomology of a point and of the Steenrod algebra of all cohomology operations.  I will describe some computations of Ext groups over the motivic Steenrod algebra (over the complex numbers).  Via the motivic Adams spectral sequence, these computations say something about motivic stable homotopy groups.

Over the real numbers, the cohomology of a point and the Steenrod algebra are also explicitly known (again due to Voevodsky).  Similar Ext computations are possible over the real numbers, but the homological algebra is trickier.

I believe that these calculations will be an important guide for further research in motivic homotopy theory.