Algebraic K-theory of elliptic cohomology
Algebraic Topology
2025-03-19 v2 K-Theory and Homology
Abstract
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.
Keywords
Cite
@article{arxiv.2204.05890,
title = {Algebraic K-theory of elliptic cohomology},
author = {Gabriel Angelini-Knoll and Christian Ausoni and Dominic Leon Culver and Eva Höning and John Rognes},
journal= {arXiv preprint arXiv:2204.05890},
year = {2025}
}
Comments
New Figure 7.1. Sections 11 and 12 rewritten as per referee's advice