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Tensor structures in the theory of modulus presheaves with transfers

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Abstract

The tensor product of \({\mathbb {A}}^1\)-invariant sheaves with transfers introduced by Voevodsky is generalized to reciprocity sheaves via the theory of modulus presheaves with transfers. We prove several general properties of this construction and compute it in some cases. In particular we obtain new (motivic) presentations of the absolute Kähler differentials and the first infinitesimal neighborhood of the diagonal.

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Notes

  1. The term lax monoidal is used in a loose sense; it seems a correct mathematical notion which appears in the literature is unbiased oplax monoidal category.

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Acknowledgements

Part of this work was done while the first author was a visiting professor at the TU München. He thanks Eva Viehmann for the invitation and the support. The project started when the third author was visiting Freie Universität Berlin. He thanks their hospitality and support.

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Authors and Affiliations

  1. Bergische Universität Wuppertal, Gaußstr 20, 42119, Wuppertal, Germany

    Kay Rülling

  2. Technische Universität München, Boltzmannstr. 3, 85748, Garching, Germany

    Kay Rülling

  3. Department of Mathematical and Physical sciences, Japan Women’s University, 2-8-1 Mejirodai, Bunkyo-ku, Tokyo, 112-8681, Japan

    Rin Sugiyama

  4. Graduate School of Science, Mathematical Institute, Tohoku University, Aoba, Sendai, 980-8578, Japan

    Takao Yamazaki

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  1. Kay Rülling
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  2. Rin Sugiyama
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  3. Takao Yamazaki
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Correspondence to Takao Yamazaki.

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The first author was supported by the DFG Heisenberg grant RU 1412/2-2. The second author is supported by JSPS KAKENHI grant (JP16K17579). The third author is supported by JSPS KAKENHI grant (JP18K03232).

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Rülling, K., Sugiyama, R. & Yamazaki, T. Tensor structures in the theory of modulus presheaves with transfers. Math. Z. 300, 929–977 (2022). https://doi.org/10.1007/s00209-021-02819-2

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