Two new motivic complexes for non-smooth schemes

TL;DR

This paper explores new motivic complexes for non-smooth schemes, comparing Elmanto-Morrow's complex with procdh sheafification, and discusses their relationships and properties.

Contribution

It introduces and compares two motivic complexes for non-smooth schemes, expanding understanding of their structures and relationships.

Findings

Comparison between Elmanto-Morrow's motivic complex and procdh sheafification.

The proof relies on main results from EM23.

Joint work with Shuji Saito.

Abstract

These are expanded notes from a talk at the RIMS Workshop, Algebraic Number Theory and Related Topics, December 13th, 2023. We discussed Elmanto-Morrow's motivic complex, the procdh sheafification of the classical motivic complex, and their comparison. The procdh topology and the comparison is joint work with Shuji Saito. The comparison was obtained through joint discussion with Morrow, and its proof relies heavily on the main results of [EM23].