11 papers
A derived Chouinard's theorem for infinite groups
Natàlia Castellana, Juan Omar Gómez
We establish a Chouinard-type theorem for modules over algebras of cochains on the classifying spaces of a broad class of infinite groups, allowing commutative ring spectra as coef…
The proper stable module category of a group algebra
Georgios Dalezios, Juan Omar Gómez
We introduce the proper stable module category for an arbitrary discrete group over any commutative ring by means of cotorsion pairs and abelian model structures. This category is…
Hopfological algebra, revisited
Juan Omar Gómez, Gustavo Jasso, Marius Nielsen
We propose an -categorical approach to Khovanov--Qi's Hopfological algebra that, in particular, refines several foundational aspects of the theory by recasting the previous…
Descent and finite permutation resolutions for discrete groups
Juan Omar Gómez, Luca Pol
Let be a discrete group with a finite-dimensional model for the classifying space for proper actions, and let be a commutative Noetherian ring of finite global dimension. I…
The classification of integral endotrivial complexes
Juan Omar Gómez, Sam K. Miller
We describe the group of endotrivial complexes, i.e., the Picard group, of the derived category of permutation modules for a finite group over a commutative Noetherian ring. As a r…
The importance of being isolated
Scott Balchin, Juan Omar Gómez, Greg Stevenson
We give both a sufficient condition for and an obstruction to the derived category of a commutative ring being generated by its residue fields. As an illustration, we exhibit a rin…
Conservative geometric functors via purity
Natàlia Castellana, Juan Omar Gómez
We establish a criterion for determining when a family of geometric functors is jointly conservative through the lens of purity in compactly generated triangulated categories. We i…
Geometric purity and the frame of smashing ideals
Juan Omar Gómez, Maurcio Medina-Barcenas, Greg Stevenson +2
We introduce the notion of geometric purity in rigidly-compactly generated tt-categories by considering exact triangles that are pure at each tt-stalk. We develop a systematic stud…
Notes on Cohomological Finite Generation for Finite Group Schemes
Juan Omar Goméz, Chris J. Parker
These are extended notes based on lectures given by Vincent Franjou, Paul Sobaje, Peter Symonds and Antoine Touzé at the Master Class on New Developments in Finite Generation of Co…
The Balmer spectrum of integral permutation modules
Umesh V Dubey, Juan Omar Gómez
We extend the analysis of Balmer and Gallauer on the tt-geometry of the small derived category of permutation modules for a finite group over a field to the setting of a commutativ…
Fiberwise building and stratification in tensor triangular geometry
Juan Omar Gómez
We establish conditions on a family of coproduct-preserving tt-functors between tt-categories with small coproducts, ensuring that the loca…