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arXiv · 2107.00381

Reciprocity sheaves and logarithmic motives

Shuji Saito
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Abstract

We connect two developments aiming at extending Voevodsky's theory of motives over a field in such a way to encompass non-$\mathbf{A}^1$-invariant phenomina. One is theory of reciprocity sheaves introduced by Kahn-Saito-Yamazaki. Another is theory of the triangulated category $\operatorname{\mathbf{logDM}}^{\operatorname{eff}}$ of logarithmic motives launched by Binda, Park and {\O}stv{\ae}r. We prove that the Nisnevich cohomology of reciprocity sheaves is representable in $\operatorname{\mathbf{logDM}}^{\operatorname{eff}}$.

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Shuji Saito. 2021-07-01. Reciprocity sheaves and logarithmic motives. https://arxiv.org/abs/2107.00381

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