A motivic construction of the de Rham-Witt complex

Junnosuke Koizumi; Hiroyasu Miyazaki

A motivic construction of the de Rham-Witt complex

Algebraic Geometry 2024-01-01 v3 Number Theory

Authors: Junnosuke Koizumi , Hiroyasu Miyazaki

Abstract

The theory of reciprocity sheaves due to Kahn-Saito-Yamazaki is a powerful framework to study invariants of smooth varieties via invariants of pairs $(X,D)$ of a variety $X$ and a divisor $D$ . We develop a generalization of this theory where $D$ can be a $\mathbb{Q}$ -divisor. As an application, we provide a motivic construction of the de Rham-Witt complex, which is analogous to the motivic construction of the Milnor $K$ -theory due to Suslin-Voevodsky.

Keywords

de Rham-Witt complex reciprocity sheaf motivic construction Q-divisor Milnor K-theory

Cite

@article{arxiv.2301.05846,
  title  = {A motivic construction of the de Rham-Witt complex},
  author = {Junnosuke Koizumi and Hiroyasu Miyazaki},
  journal= {arXiv preprint arXiv:2301.05846},
  year   = {2024}
}

Comments

31 pages, typos corrected, to appear in Journal of Pure and Applied Algebra

A motivic construction of the de Rham-Witt complex

Abstract

Keywords

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