Let G be a finite group and let F be a family of subgroups of G. We introduce a class of G-
equivariant spectra that we call F-nilpotent. This definition fits into the general theory of …

To a “stable homotopy theory”(a presentable, symmetric monoidal stable∞-category), we
naturally associate a category of finite étale algebra objects and, using Grothendieck's …

This paper starts with an exposition of descent-theoretic techniques in the study of Picard
groups of E∞–ring spectra, which naturally lead to the study of Picard spectra. We then …

We explore the C 2–equivariant spectra Tmf 1 (3) and TMF 1 (3). In particular, we compute
their C 2–equivariant Picard groups and the C 2–equivariant Anderson dual of Tmf 1 (3) …

Let A→ B be a G-Galois extension of rings, or more generally of E∞-ring spectra in the
sense of Rognes. A basic question in algebraic K-theory asks how close the map K (A)→ K …

We develop a general theory of higher semiadditive Fourier transforms that includes both
the classical discrete Fourier transform for finite abelian groups at height-modules [-12pc] …

The cohomology theory known as Tmf Tmf, for “topological modular forms,” is a universal
object mapping out to elliptic cohomology theories, and its coefficient ring is closely …

We compute the mod $2 $ homology of the spectrum $\mathrm {tmf} $ of topological modular
forms by proving a 2-local equivalence $\mathrm {tmf}\wedge DA (1)\simeq\mathrm {tmf} _1 …

For a finite abelian group A, we determine the Balmer spectrum of Sp _A^ ω Sp A ω, the
compact objects in genuine A-spectra. This generalizes the case A= Z/p ZA= Z/p Z due to …

We prove a purity property in telescopically localized algebraic $ K $-theory of ring spectra:
For $ n\geq 1$, the $ T (n) $-localization of $ K (R) $ only depends on the $ T …