Motifs in Derived Algebraic Geometry

TL;DR

This paper introduces a formal framework for motifs in derived algebraic geometry, enabling the construction of derived stacks without needing derived extensions, thus simplifying the theoretical landscape.

Contribution

It formalizes the concept of motifs as sheaves on a model site and constructs derived algebraic stacks functorially, removing the need for derived extensions.

Findings

Formalization of motifs as sheaves on a model site

Construction of derived algebraic stacks from motifs

Elimination of the necessity for derived extensions

Abstract

We formalize the concept of sheaves of sets on a model site by considering variables thereof, or motifs, and we construct functorially defined derived algebraic stacks from them, thereby eliminating the necessity to choose derived extensions.