# 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

Time   12:10

Date:  Monday, November 20, 2018

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 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).

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