Motivic real topological Hochschild spectrum

Park, Doosung

doi:10.2140/agt.2026.26.1867

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ISSN (electronic): 1472-2739

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Motivic real topological Hochschild spectrum

Doosung Park

Algebraic & Geometric Topology 26 (2026) 1867–1905

DOI: 10.2140/agt.2026.26.1867

Abstract

We define real topological Hochschild homology of separated log schemes with involutions. We show that real topological Hochschild homology is $(ℙ^{n}, ℙ^{n - 1})$ -invariant, which leads to the definition of the motivic real topological Hochschild spectrum living in a certain $ℤ ∕ 2$ -equivariant logarithmic motivic category. We explore properties of real topological Hochschild homology that can be deduced from the logarithmic motivic homotopy theory. We also define the motivic real topological cyclic spectrum.

Keywords

real topological Hochschild homology, logarithmic schemes, logarithmic motivic homotopy theory

Mathematical Subject Classification

Primary: 19D55

Secondary: 11E70, 14A21, 16E40, 55P91

References

Publication

Received: 6 June 2024

Revised: 30 April 2025

Accepted: 31 May 2025

Published: 23 May 2026

Authors

Doosung Park
Department of Mathematics and Informatics Bergische Universität Wuppertal Wuppertal Germany

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Volume 26, issue 5 (2026)