2014/06/19 by Akhil Mathew, Mathew, Akhil
Mathematics · #Algebraic Geometry and Number Theory #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #Category Theory (math.CT) #Commutative Algebra (math.AC) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.1406.4947
openalex publication_date 2014/06/19 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
Let A be an E∞-ring spectrum over the rational numbers. If A satisfies a noetherian condition on its homotopy groups π_*(A), we construct a collection of E∞-A-algebras that realize on homotopy the residue fields of π_*(A). We prove an analog of the nilpotence theorem for these residue fields. As a result, we are able to give a complete algebraic description of the Galois theory of A and of the thick subcategories of perfect A-modules. We also obtain partial information on the Picard group of A.