Cancellation theorem for motivic spaces with finite flat transfers

TL;DR

This paper proves that motivic spaces with finite flat transfers over a perfect field satisfy key properties of motives, including an analog of Voevodsky's cancellation theorem, advancing the theoretical framework of motivic homotopy theory.

Contribution

It establishes that the category of motivic spaces with finite flat transfers satisfies expected properties and proves an analog of Voevodsky's cancellation theorem.

Findings

Category satisfies properties of motives

Proves analog of Voevodsky's cancellation theorem

Supports development of motivic homotopy theory

Abstract

We show that the category of motivic spaces with transfers along finite flat morphisms, over a perfect field, satisfies all the properties we have come to expect of good categories of motives. In particular we establish the analog of Voevodsky's cancellation theorem.