Algebraic K-theory of elliptic cohomology
Abstract
We calculate the mod (p, v1, v2) homotopy V(2)* TC(BP<2>) of the topological cyclic homology of the truncated Brown--Peterson spectrum BP<2>, at all primes p7, and show that it is a finitely generated and free Fp[v3]-module on 12p+4 generators in explicit degrees within the range -1 * 2p3+2p2+2p-3. At these primes BP<2> is a form of elliptic cohomology, and our result also determines the mod (p, v1, v2) homotopy of its algebraic K-theory. Our computation is the first that exhibits chromatic redshift from pure v2-periodicity to pure v3-periodicity in a precise quantitative manner.
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