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Pré-Publication, Document De Travail (Preprint/Prepublication) Année : 2022

Algebraic K-theory of elliptic cohomology

Résumé

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 F_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.

Dates et versions

hal-03861399 , version 1 (19-11-2022)

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Gabriel Angelini-Knoll, Christian Ausoni, Dominic Leon Culver, Eva Höning, John Rognes. Algebraic K-theory of elliptic cohomology. 2022. ⟨hal-03861399⟩
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