Algebraic K-theory of elliptic cohomology

Date: 2022-04-12

Time: 14:15 - 16:00


John Rognes


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 pge7, 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.