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arXiv · 2309.11463

Algebraic K-theory of real topological K-theory

Gabriel Angelini-Knoll·Christian Ausoni·John Rognes
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Abstract

We determine the A(1)-homotopy of the topological cyclic homology of the connective real K-theory spectrum ko. The answer has an associated graded that is a free F_2[v_2^4]-module of rank 52, on explicit generators in stems -1 \le * \le 30. The calculation is achieved by using prismatic and syntomic cohomology of ko as introduced by Hahn-Raksit-Wilson, extending work of Bhatt-Morrow-Scholze from the case of classical commutative rings to E_\infty rings. A new feature in our case is that there are nonzero differentials in the motivic spectral sequence from syntomic cohomology to topological cyclic homology.

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Gabriel Angelini-Knoll, Christian Ausoni, John Rognes. 2023-09-20. Algebraic K-theory of real topological K-theory. https://arxiv.org/abs/2309.11463

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