Algebra/Topology Seminar

Speaker: Lior Yanovski (The Hebrew University of Jerusalem)

Title: Higher semi-additivity in chromatic homotopy theory.

Abstract: In ordinary algebra, characteristic zero behaves differently from characteristic p>0, partially due to the possibility to symmetrize finite group actions. In particular, given a finite group G acting on a rational vector space V, the "norm map" from the co-invariants V_G to the invariants V^G is an isomorphism (in marked contrast to the positive characteristic case). In the chromatic world, the Morava K-theories provide an interpolation between the zero characteristic (represented by rational cohomology) and positive characteristic (represented by F_p cohomology). A classical result of Hovey-Sadofsky-Greenlees shows that the norm map is still an isomorphism in these "intermediate characteristics". A subsequent work of Hopkins and Lurie vastly generalises this result and puts it in the context of a new formalism of "higher semiadditivity" (a.k.a. "ambidexterity"). I will describe a joint work with Tomer Schlank and Shachar Carmeli in which we generalize the results of Hopkins-Lurie and extend them among other things to the telescopic localizations and draw some consequences (along the way, we obtain a new and more conceptual proof for their original result).