Multiplicative transfers in the cohomology of algebraic varieties

Algebro-Geometric and Homotopical Methods

26 January 11:00 - 12:00

Marc Hoyois - Massachusetts Institute of Technology, MIT

Given a finite covering space E → B, there is in ordinary cohomology an additive transfer map H^n(E) → H^n(B) which specializes to addition when E is a sum of copies of B. Such transfers exist more generally for any cohomology theory represented by an E_∞-space. More subtle is a multiplicative transfer map H^*(E) → H^*(B), generalizing the cup product, which comes from the fact that cohomology is represented by an E_∞-ring spectrum. There are similar phenomena in equivariant and motivic homotopy theory, but in these cases the analog of an E_∞-ring spectrum is a more complicated structure. It turns out that many motivic E_∞-ring spectra (eg those representing motivic cohomology, algebraic K-theory, and algebraic cobordism) possess this extra structure, and this leads to various multiplicative transfer maps in these cohomology theories. This is joint work with Tom Bachmann.
Eric M. Friedlander
University of Southern California
Lars Hesselholt
University of Copenhagen
Paul Arne Østvaer
University of Oslo


Paul Arne Østvaer


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