Report on 𝔼_∞-descendability

2025/08/18 by Antieau, Benjamin, Stefanich, Germán
#Algebraic Geometry (math.AG) #Algebraic Topology (math.AT) #FOS: Mathematics

paper · doi:10.48550/arxiv.2508.13089

Abstract

We introduce the notion of 𝔼_∞-descendability as well as a derived variant. We prove that several classes of descendable maps of commutative rings are 𝔼_∞-descendable. As an application, we prove a variant of Tannaka duality.

Citations

• Descendability of Faithfully Flat Covers of Perfect Stacks
• On cohomology of locally profinite sets
• Spherical Witt vectors and integral models for spaces
• Unipotent homotopy theory of schemes
• Jeff Smith's Theory of Ideals
• Hochschild homology and the derived de Rham complex revisited
• Topological Hochschild homology and integral p-adic Hodge theory
• La conjecture du facteur direct
• Examples of descent up to nilpotence
• Nilpotence and descent in equivariant stable homotopy theory
• Projectivity of the Witt vector affine Grassmannian
• Tannaka duality revisited
• Algebraization and Tannaka duality
• The Galois group of a stable homotopy theory
• Smith ideals of structured ring spectra
• Sheaves of categories and the notion of 1-affineness
• Higher Topos Theory

Related

• Indivisible Sequences and Descendability
• Tannaka duality over ring spectra
• Faithfully flat ring maps are not descendable
• Descent via Tannaka duality
• Notes on derived algebraic geometry