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Steinberg symbols and reciprocity sheaves

Junnosuke Koizumi

Vol. 7 (2022), No. 4, 695–730
DOI: 10.2140/akt.2022.7.695
Abstract

We study multilinear symbols on fields taking values in reciprocity sheaves. We prove that any such symbol satisfying natural axioms automatically has Steinberg-type relations, which is a manifestation of the geometry of modulus pairs lying behind.

Keywords
reciprocity sheaf, Suslin homology with modulus, nonhomotopy invariant motive
Mathematical Subject Classification
Primary: 14F42
Secondary: 19D45
Milestones
Received: 2 September 2021
Revised: 14 September 2022
Accepted: 2 October 2022
Published: 15 March 2023
Authors
Junnosuke Koizumi
Graduate School of Mathematical Sciences
University of Tokyo
Tokyo
Japan