Thursday, Geometry and Topology Seminar, 20 Dec, Lior Yanovski . Title ” Higher semi-additivity and chromatic homotopy theory “
Geometry & Topology Seminar
Speaker: Lior Yanovski (The Hebrew University of Jerusalem)
Topic: Higher semi-additivity and chromatic homotopy theory
Place: room 614 in the Science & Education Building
Date: Monday, November 20, 2018
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 dimensional 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 a 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 ismorphism 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. “amidexterity”). I will describe a joint work with Tomer Schlank and Shachar Carmeli in which we generalize the results of Hopkins-Lurie and extend them to the telescopic localizations and draw some consequences (along the way, we obtain a new and more conceptual proof for their original result).