Seminar

# Algebraic K-theory of elliptic cohomology

#### John Rognes - University of Oslo

Joint work with G. Angelini-Knoll, Ch. Ausoni, D.L. Culver and E. H{\"o}ning. We calculate the mod (p, v_1, v_2) homotopy V(2)_* TC(BP<2>) of the topological cyclic homology of the truncated Brown-Peterson spectrum BP<2>, at all primes p\ge7, and show that it is a finitely generated and free \bF_p[v_3]-module on 12p+4 generators in explicit degrees within the range -1 \le * \le 2p^3+2p^2+2p-3. At these primes BP<2> is a form of elliptic cohomology, and our result also determines the mod (p, v_1, v_2) homotopy of its algebraic K-theory. Our computation is the first that exhibits chromatic redshift from pure v_2-periodicity to pure v_3-periodicity in a precise quantitative manner.

Organizers
Gregory Arone
Stockholm University
Tilman Bauer
KTH Royal Institute of Technology
Alexander Berglund
Stockholm University
Søren Galatius
University of Copenhagen
Jesper Grodal,
University of Copenhagen
Thomas Kragh
Uppsala University

# ProgramContact

Alexander Berglund

alexb@math.su.se

Søren Galatius

galatius@math.ku.dk

Thomas Kragh

thomas.kragh@math.uu.se

# Otherinformation

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