Tensor structures in the theory of modulus presheaves with transfers
type: Item
instance of: scholarly article
title: Tensor structures in the theory of modulus presheaves with transfers
zbMATH Open document ID: 1492.14034
author: Kay Rülling
author: R. Sugiyama
author: Takao Yamazaki
published in: Mathematische Zeitschrift
publication date: 2022-01-25T00:00:00Z
full work available at URL: https://arxiv.org/abs/1911.05291
review text: Consider the diagram \[ \begin{tikzcd} \textbf{Cor} \arrow[r, equal] \arrow[d, "\mathbb{Z}_{tr}"] & \textbf{Cor} \arrow[d, "\mathbb{Z}_{tr}"] & \textbf{MCor} \arrow[l, "\omega"] \arrow[d, "\mathbb{Z}_{tr}"] \\ \textbf{PST} \arrow[d, shift left= 1ex, "h_0^{\mathbb{A}^1}"] \arrow[r, equal] & \textbf{PST} \arrow[r, shift left= 1ex, "\omega^*"] \arrow[d, shift left= 1ex, "\rho"] & \textbf{MPST} \arrow[l, shift left= 1ex, "\omega_!"] \arrow[d, shift left= 1ex, "h_0^{\overline{\boxempty}}"] \\ \textbf{HI} \arrow[u, hookrightarrow, shift left= 1ex, "\iota^{\mathbb{A}^1}"] \arrow[r, hookrightarrow, shift left= 1ex] & \textbf{RSC} \arrow[u, hookrightarrow, shift left= 1ex, "\iota^{\natural}"] \arrow[l, shift left= 1ex, "h_0^{rec}"] \arrow[r, shift left= 1ex, "\omega^{\textbf{CI}}"] & \textbf{CI} \arrow[u, hookrightarrow, shift left= 1ex, "\iota^{\overline{\boxempty}}"] \arrow[l, shift left= 1ex, "\omega_{\textbf{CI}}=\omega_!"] \end{tikzcd} \] where: \begin{itemize} \item \(\textbf{Cor}\) is Voedosky's category of finite correspondences whose objects are smooth varieties over a perfect base field \(k\), \item \(\textbf{PST}\) the category of presheaves over \(\textbf{Cor}\), \item \(\textbf{HI}\) is the full subcategory of \(\textbf{PST}\) consisting of \(\mathbb{A}^1\)-invariant presheaves, \item \(\textbf{MCor}\) is the category whose objects are proper modulus pairs \(M=(\overline{M}, M^{\infty})\), \item \(\textbf{MPST}\) the category of presheaves over \(\textbf{MCor}\), \item \(\textbf{CI}\) the full subcategory of \(\textbf{MPST}\) consisting of \(\overline{\boxempty}\)-invariant presheaves (with \(\overline{\boxempty} = ( \mathbb{P}^1, (\infty))\)), \item \(\textbf{RSC}\) is the full subcategory of \(\textbf{PST}\) consisting of presheaves having SC-reciprocity, \item and where the functors are the obvious ones. \end{itemize} The column on the left consists of well-known categories defined by \textit{V. Voevodsky} [Ann. Math. Stud. 143, 87--137 (2000; Zbl 1019.14010)…
reviewed by: Niels Feld
Mathematics Subject Classification ID: 14F42
Mathematics Subject Classification ID: 19E15
Mathematics Subject Classification ID: 19D45
zbMATH DE Number: 7463813
zbMATH Keywords: Suslin homology with modulus
zbMATH Keywords: non-homotopy invariant motive
zbMATH Keywords: Somekawa \(K\)-group
MaRDI profile type: Publication
OpenAlex ID: W3185898334
arXiv ID: 1911.05291
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DOI: 10.1007/S00209-021-02819-2
description: scientific article