Algebraic Models for Quasi-Coherent Sheaves in Spectral Algebraic Geometry

TL;DR

This paper develops an algebraic framework for understanding quasi-coherent sheaves on complex spectral stacks, bridging stable homotopy theory and spectral algebraic geometry through adapted homology theories.

Contribution

It introduces an algebraic model for quasi-coherent sheaves on non-connective spectral stacks, expanding the tools available in spectral algebraic geometry.

Findings

Established an algebraic model for sheaves on spectral stacks

Connected homotopy theory with algebraic geometry techniques

Provided new methods for studying non-connective geometric stacks

Abstract

In this paper we prove the existence of an algebraic model for quasi-coherent sheaves on certain non-connective geometric stacks arising in stable homotopy theory and spectral algebraic geometry using the machinery of adapted homology theories.