7 papers · 1 filter
Exponential motives on the affine Grassmannian
Robert Cass, Thibaud van den Hove, Jakob Scholbach
We develop a notion of exponential motives on general prestacks equipped with a -action, and compare them with Whittaker motives via Gaitsgory's Kirillov model. We th…
Categorical Künneth formulas for cohomological motives
Timo Richarz, Jakob Scholbach
The manuscript at hand systematically studies Künneth formulas at a categorical level. We give criteria for an abstract six functor formalism to satisfy the categorical Künneth for…
Frobenius rigidity in -homotopy theory
Timo Richarz, Jakob Scholbach
We study the homotopy fixed points under the Frobenius endomorphism on the stable -homotopy category of schemes in characteristic and prove a rigidity result for…
Central motives on parahoric flag varieties
Robert Cass, Thibaud van den Hove, Jakob Scholbach
We construct a refinement of Gaitsgory's central functor for integral motivic sheaves, and show it preserves stratified Tate motives. Towards this end, we develop a reformulation o…
Constructible sheaves on schemes
Tamir Hemo, Timo Richarz, Jakob Scholbach
We present a uniform theory of constructible sheaves on arbitrary schemes with coefficients in topological or even condensed rings. This is accomplished by defining lisse sheaves t…
Integral Motivic Sheaves And Geometric Representation Theory
Jens Niklas Eberhardt, Jakob Scholbach
With representation-theoretic applications in mind, we construct a formalism of reduced motives with integral coefficients. These are motivic sheaves from which the higher motivic…