50 citations · 146 across the 21 of their papers we have counts for
21 papers
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…
The geometric Satake equivalence for integral motives
Robert Cass, Thibaud van den Hove, Jakob Scholbach
We prove the geometric Satake equivalence for mixed Tate motives over the integral motivic cohomology spectrum. This refines previous versions of the geometric Satake equivalence f…
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…
A categorical Künneth formula for constructible Weil sheaves
Tamir Hemo, Timo Richarz, Jakob Scholbach
We prove a Künneth-type equivalence of derived categories of lisse and constructible Weil sheaves on schemes in characteristic for various coefficients, including finite di…
Tate motives on Witt vector affine flag varieties
Timo Richarz, Jakob Scholbach
Relying on recent advances in the theory of motives we develope a general formalism for derived categories of motives with Q-coefficients on perfect (ind-)schemes. As an applicatio…
The motivic Satake equivalence
Timo Richarz, Jakob Scholbach
We refine the geometric Satake equivalence due to Ginzburg, Beilinson-Drinfeld, and Mirković-Vilonen to an equivalence between mixed Tate motives on the double quotient $L^+ G \bac…
The intersection motive of the moduli stack of shtukas
Timo Richarz, Jakob Scholbach
For a split reductive group G over a finite field, we show that the intersection (cohomology) motive of the moduli stack of iterated G-shtukas with bounded modification and level s…
Modules over the de Rham cohomology spectrum
Dmitri Pavlov, Jakob Scholbach
We show that the bounded derived category of regular holonomic D-modules on a smooth variety is equivalent to the homotopy catgory of compact (or constructible) modules over the mo…
Homotopy theory of symmetric powers
Dmitri Pavlov, Jakob Scholbach
We introduce the symmetricity notions of symmetric h-monoidality, symmetroidality, and symmetric flatness. As shown in our paper arXiv:1410.5675, these properties lie at the heart…
Symmetric operads in abstract symmetric spectra
Dmitri Pavlov, Jakob Scholbach
This paper sets up the foundations for derived algebraic geometry, Goerss--Hopkins obstruction theory, and the construction of commutative ring spectra in the abstract setting of o…
Admissibility and rectification of colored symmetric operads
Dmitri Pavlov, Jakob Scholbach
We establish a highly flexible condition that guarantees that all colored symmetric operads in a symmetric monoidal model category are admissible, i.e., the category of algebras ov…
Arakelov motivic cohomology II
Jakob Scholbach
We show that the constructions done in part I generalize their classical counterparts: firstly, the classical Beilinson regulator is induced by the abstract Chern class map from $B…
Algebraic K-theory of the infinite place
Jakob Scholbach
In this note, we show that the algebraic K-theory of generalized archimedean valuation rings occurring in Durov's compactification of the spectrum of a number ring is given by stab…
Arakelov motivic cohomology I
Andreas Holmstrom, Jakob Scholbach
This paper introduces a new cohomology theory for schemes of finite type over an arithmetic ring. The main motivation for this Arakelov-theoretic version of motivic cohomology is t…
Mixed Artin-Tate motives over number rings
Jakob Scholbach
This paper studies Artin-Tate motives over number rings. As a subcategory of geometric motives, the triangulated category of Artin-Tate motives DATM(S) is generated by motives of s…
f-cohomology and motives over number rings
Jakob Scholbach
This paper is concerned with an interpretation of f-cohomology, a modification of motivic cohomology of motives over number fields, in terms of motives over number rings. Under sta…
Special L-values of geometric motives
Jakob Scholbach
This paper proposes a conjecture on special values of L-functions of geometric motives over Z. This includes L-functions of mixed motives over Q and Hasse-Weil zeta-functions of sc…