Spectral Excision and Descent for Almost Perfect Complexes

TL;DR

This paper demonstrates that almost perfect complexes of commutative ring spectra satisfy excision and v-descent, extending classical results to a derived setting and broadening their applicability.

Contribution

It generalizes Milnor excision and v-descent to almost perfect complexes of commutative ring spectra, unifying and extending previous results in derived algebraic geometry.

Findings

Almost perfect complexes satisfy excision.

Almost perfect complexes satisfy v-descent.

Generalization of classical descent results.

Abstract

We show that almost perfect complexes of commutative ring spectra satisfy excision and $v$-descent. These results generalize Milnor excision for perfect complexes of ordinary commutative rings and $v$-descent for almost perfect complexes of locally noetherian derived stacks by Halpern-Leistner and Preygel, respectively.