David Gepner

An ∞-categorical approach to R-line bundles, R-module Thom spectra, and twisted R-homology

We develop a generalization of the theory of Thom spectra using the language of infinity categories. This treatment exposes the conceptual underpinnings of the Thom spectrum functor: we use a new model of parametrized spectra, and our definition is motivated by the geometric definition of Thom spectra of May-Sigurdsson. For an associative ring spectrum

Brauer groups and étale cohomology in derived algebraic geometry

R

Enriched ∞-categories via non-symmetric ∞-operads

, we associate a Thom spectrum to a map of infinity categories from the infinity groupoid of a space

Universality of multiplicative infinite loop space machines

X

Units of ring spectra, orientations, and Thom spectra via rigid infinite loop space theory

to the infinity category of free rank one

A universal characterization of higher algebraic K-theory

R

Units of ring spectra and Thom spectra

-modules, which we show is a model for

On the Motivic Spectra Representing Algebraic Cobordism and Algebraic K-Theory

BGL_1 R

Homotopy Theory of Orbispaces

; we show that

Twists of K-theory and TMF

BGL_1 R