Seminars - Page 4

Time and place: , B71 NHA

Abstract: We introduce the notion of Arakelov motivic cohomology, and discuss the beautiful reformulation (due to Jakob Scholbach) of the Beilinson conjectures on special values of L-functions. 

Time and place: , B71 NHA

Abstract: In topology, there is a correspondence between generalized cohomology theories (in the sense of the Eilenberg-Steenrod axioms) on one hand and spectra on the other hand, the latter being objects in the stable homotopy category SH. In algebraic geometry and motivic homotopy theory, the situation is much more complicated in several ways. Firstly, there are many stable homotopy categories, one for each scheme, and various functors between them. Secondly, there are many sets of axioms for what a cohomology theory should be (Weil cohomology, Bloch-Ogus cohomology, oriented cohomology, ...) and a huge zoo of cohomology theories. The aim of the talk will be to give an overview of all generalized cohomology theories in algebraic geometry, using the language of motivic stable homotopy theory. 

Time and place: , B63 NHA

We study a modified version of Rognes' logarithmic structures on structured ring spectra. In our setup, we obtain canonical logarithmic structures on connective K-theory spectra which approximate the respective periodic spectra. The inclusion of the p-complete Adams summand into the p-complete connective complex K-theory spectrum is compatible with these logarithmic structures. The vanishing of appropriate logarithmic topological Andre-Quillen homology groups confirms that the inclusion of the Adams summand should be viewed as a tamely ramified extension of ring spectra. 

Time and place: , B 62 NHA

I extend my 2005 AG&T paper with Bruner from the circle case to more general Lie groups.  There are new results about infinite cycles for actions by the torus T2 or the rotation group SO(3). 

Time and place: , B 62 NHA

I will go through the simplest case of my 2005 AG&T paper with Bruner, showing that certain classes, in the homological homotopy fixed point spectral sequence for a circle action on a commutative ring spectrum, are infinite cycles. The idea of using an universal example may lead to generalizations for actions by tori or other Lie groups. 

Time and place: , B 62 NHA

We show that the hermitian K-theory of regular schemes (with 2 a unit in the ring of regular functions) is represented in the A^1-homotopy category of Morel-Voevodsky by the ind-scheme of non-degenerate Grassmanians.