Steinberg symbols and reciprocity sheaves
Junnosuke Koizumi
TL;DR
This paper investigates multilinear symbols on fields within reciprocity sheaves, demonstrating that natural axioms enforce Steinberg relations, revealing geometric structures related to modulus pairs.
Contribution
It establishes that multilinear symbols satisfying certain axioms inherently obey Steinberg relations, linking algebraic symbols to geometric structures.
Findings
Symbols satisfy Steinberg relations under natural axioms
Reveals geometric interpretation via modulus pairs
Connects algebraic symbols with reciprocity sheaves
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.
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Taxonomy
TopicsTopological and Geometric Data Analysis · Mathematical Dynamics and Fractals · Homotopy and Cohomology in Algebraic Topology