36 citations · 68 across the 9 of their papers we have counts for
10 papers
Local Gorenstein duality for cochains on spaces
Tobias Barthel, Natalia Castellana, Drew Heard +1
We investigate when a commutative ring spectrum satisfies a homotopical version of local Gorenstein duality, extending the notion previously studied by Greenlees. In order to d…
Thom spectra, higher and tensors in -categories
Nima Rasekh, Bruno Stonek, Gabriel Valenzuela
Let be a map of -groups, where denotes the Picard space of an -ring spectrum . We determine the tensor $X\otimes_R…
On stratification for spaces with Noetherian mod cohomology
Tobias Barthel, Natalia Castellana, Drew Heard +1
Let be a topological space with Noetherian mod cohomology and let be the commutative ring spectrum of -valued cochains on . The goal…
Derived completion for comodules
Tobias Barthel, Drew Heard, Gabriel Valenzuela
The objective of this paper is to introduce and study completions and local homology of comodules over Hopf algebroids, extending previous work of Greenlees and May in the discrete…
Stratification and duality for homotopical groups
Tobias Barthel, Natalia Castellana, Drew Heard +1
We generalize Quillen's -isomorphism theorem, Quillen's stratification theorem, the stable transfer, and the finite generation of cohomology rings from finite groups to homotopi…
The algebraic chromatic splitting conjecture for Noetherian ring spectra
Tobias Barthel, Drew Heard, Gabriel Valenzuela
We formulate a version of Hopkins' chromatic splitting conjecture for an arbitrary structured ring spectrum , and prove it whenever is Noetherian. As an application, thes…