Tobias Barthel

Local duality for structured ring spectra

Abstract We use the abstract framework constructed in our earlier paper [8] to study local duality for Noetherian E ∞ -ring spectra. In particular, we compute the local cohomology of relative dualizing modules for finite morphisms of ring spectra, thereby generalizing the local duality theorem of Benson and Greenlees. We then explain how our results apply to the modular representation theory of compact Lie groups and finite group schemes, which recovers the theory previously developed by Benson, Iyengar, Krause, and Pevtsova.

The character of the total power operation

In this paper we compute the total power operation for the Morava

Local duality in algebra and topology

E

Brown-Peterson cohomology from Morava E-theory

-theory of any finite group up to torsion. Our formula is stated in terms of the

Auslander–Reiten Sequences, Brown–Comenetz Duality, and the K(n)-local Generating Hypothesis

GL_n(Q_p)

Algebraic chromatic homotopy theory for BP∗BP-comodules: ALGEBRAIC CHROMATIC HOMOTOPY THEORY FOR BP∗BP-COMODULES

-action on the Drinfeld ring of full level structures on the formal group associated to

The algebraic chromatic splitting conjecture for Noetherian ring spectra

E

A SIMPLE UNIVERSAL PROPERTY OF THOM RING SPECTRA

-theory. It can be specialized to give explicit descriptions of many classical operations. Moreover, we show that the character map of Hopkins, Kuhn, and Ravenel from

On localization sequences in the algebraic K-theory of ring spectra

E

The chromatic splitting conjecture for Noetherian commutative ring spectra

-theory to