Related papers: Springer Motives

Let $G$ be a reductive group over $\mathbb{F}_{p}$ with associated finite group of Lie type $G^{F}$. Let $T$ be a maximal torus contained inside a Borel $B$ of $G$. We relate the (rational) Tate motives of $\text{B}G^{F}$ with the…

Two semisimple algebraic groups of the same type are said to be motivic equivalent if the motives of the associated projective homogeneous varieties of the same type are isomorphic. We give general criteria of motivic equivalence in terms…

We define the categories of log motives and log mixed motives. The latter gives a new formulation for the category of mixed motives. We prove that the former is a semisimple abelian category if and only if the numerical equivalence and…

We analyze the tt-geometry of derived Artin motives, via modular representation theory of profinite groups. To illustrate our methods, we discuss Artin motives over a finite field, in which case we also prove stratification.

We prove that the category of countable Tate modules over an arbitrary discrete ring embeds fully faithfully into that of condensed modules. If the base ring is of finite type, we characterize the essential image as generated by the free…

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 cohomology of the base scheme has been removed. We show that…

This is not standard in the sense that we understand a Springer map to be a collapsing of homogeneous bundles. Apart from that we use mostly techniques from Chriss and Ginzbergs book but we work in the equivariant derived category of…

In this article we compute the motive associated to a cellular fibration $\Gamma$ over a smooth scheme $X$ inside Veovodsky's motivic categories. We implement this result to study the motive associated to a $G$-bundle, and additionally to…

We construct a co-$t$-structure on the derived category of coherent sheaves on the nilpotent cone $\mathcal{N}$ of a reductive group, as well as on the derived category of coherent sheaves on any parabolic Springer resolution. These…

We study a class of representations over the degenerate double affine Hecke algebra of gl_n by an algebraic method. As fundamental objects in this class, we introduce certain induced modules and study some of their properties. In…

The flag variety of a complex reductive linear algebraic group G is by definition the quotient G/B by a Borel subgroup. It can be regarded as the set of Borel subalgebras of Lie(G). Given a nilpotent element e in Lie(G), one calls Springer…

Recall that the Springer correspondence relates representations of the Weyl group to perverse sheaves on the nilpotent cone. We explain how to extend this to an equivalence between the triangulated category generated by the Springer…

Let $E/\mathbb{Q}$ be a totally real number field that is Galois over $\mathbb{Q}$, and let $\pi$ be a cuspidal, nondihedral automorphic representation of $\mathrm{GL}_2(\mathbb{A}_E)$ that is in the lowest weight discrete series at every…

This paper concerns the Algebraic Sato--Tate and Sato--Tate conjectures, based on Serre's original motivic formulation, with an eye towards explicit computations of Sato--Tate groups. We build on the algebraic framework for the Sato--Tate…

We study the motive of the moduli space of semistable Higgs bundles of coprime rank and degree on a smooth projective curve C over a field k under the assumption that C has a rational point. We show this motive is contained in the thick…

The goal of this paper is to give an explicit description of the triangulated categories of Tate and Artin-Tate motives with finite coefficients Z/m over a field K containing a primitive m-root of unity as the derived categories of exact…

Classical polylogarithms give rise to a variation of mixed Hodge-Tate structures on the punctured projective line $S=\mathbb{P}^1\setminus \{0, 1, \infty\}$, which is an extension of the symmetric power of the Kummer variation by a trivial…

Let $\mathbf{G}$ be a connected split reductive group over a field of characteristic zero or sufficiently large characteristic, $\gamma_0\in(\operatorname{Lie}\mathbf{G})((t))$ be any topologically nilpotent regular semisimple element, and…

In this paper we define the triangulated category of motives over a simplicial scheme. The morphisms between the Tate objects in this category compute the motivic cohomology of the underlying scheme. In the last section we consider the…

We analyze the spectrum of the tensor-triangulated category of Artin-Tate motives over the base field R of real numbers, with integral coefficients. Away from 2, we obtain the same spectrum as for complex Tate motives, previously studied by…