Toward a Galois theory of the integers over the sphere spectrum

Abstract

Recent work in higher algebra allows the reinterpretation of a classical description of the Eilenberg-MacLane spectrum $H\mathbb{Z}$ as a Thom spectrum, in terms of a kind of derived Galois theory. This essentially expository talk summarizes some of this work, and suggests an interpretation in terms of configuration spaces and monoidal functors on them, with some analogies to a topological field theory.

Exposition further clarified thanks to referee comments, typos corrected

References in corpus (5)

• An $\infty$-categorical approach to $R$-line bundles, $R$-module Thom spectra, and twisted $R$-homology
• The frame of smashing tensor-ideals
• Operads of genus zero curves and the Grothendieck-Teichmüller group
• An algebraic introduction to the Steenrod algebra
• Topological Hochschild Homology of H(Z/p^k)