Real Topological Hochschild Homology of Schemes

Abstract

We prove that real topological Hochschild homology $\mathrm {THR}$ for schemes with involution satisfies base change and descent for the ${\mathbb {Z}/2}$ -isovariant étale topology. As an application, we provide computations for the projective line (with and without involution) and the higher-dimensional projective spaces.

Addendum: Real Topological Hochschild Homology of Schemes

“…The only statement in [3] where this proposition is used is the following one in the proof of [3,Proposition 3.2.2], for which we now provide an alternative proof.…”

“…For commutative rings A in which 2 is invertible, as well as for , [3, Proposition 2.3.5] is true. However, for some rings A in which 2 is not invertible, the result is not correct as stated.…”

“…Hence, we have the short exact sequence where denotes the Frobenius (i.e., the squaring map). In particular, [3, Proposition 2.3.5] holds if and only if is surjective.…”