Related papers: Tensor structure on perverse Nori motives

We prove a generic smoothness result in rigid analytic geometry over a characteristic zero nonarchimedean field. The proof relies on a novel notion of generic points in rigid analytic geometry which are well-adapted to "spreading out"…

In this article we further the study of non-commutative motives. Our main result is the construction of a symmetric monoidal structure on the localizing motivator Mot of dg categories. As an application, we obtain : (1) a computation of the…

Considering a (co)homology theory $\mathbb{T}$ on a base category $\mathcal{C}$ as a fragment of a first-order logical theory we here construct an abelian category $\mathcal{A}[\mathbb{T}]$ which is universal with respect to models of…

We introduce and study the category of modular (i.e. with coefficient of positive characteristic) monodromic perverse sheaves on complex stratified $T$-varieties, with $T$ a complex algebraic torus. In particular, we show that under…

We introduce irregular constructible sheaves, which are $\mathbb{C}$-constructible with coefficients in a finite version of Novikov ring $\Lambda$ and special gradings. We show that the bounded derived category of cohomologically irregular…

Bezrukavnikov (later together with Arinkin) recovered the work of Deligne defining perverse $t$-structures for the derived category of coherent sheaves on a projective variety. In this text we prove that these $t$-structures can be obtained…

The category of effective $Witt$-motives $DWM^-(k)$ with functor $WM\colon Sm_k\to DWM^-(k)$ defining motives of smooth affine varieties for perfect field $k$, $char k\neq 2$ is constructed. In the construction Voevodsky-Suslin method is…

Recently, Levine constructed a DG category whose homotopy category is equivalent to the full subcategory of motives over a base-scheme $S$ generated by the motives of smooth projective $S$-schemes, assuming that $S$ is itself smooth over a…

A mixed Weil cohomology with values in an abelian rigid tensor category is a cohomological functor on Voevodsky's category of motives which is satisfying K\"unneth formula and such that its restriction to Chow motives is a Weil cohomology.…

The convolution powers of a perverse sheaf on an abelian variety define an interesting family of branched local systems whose geometry is still poorly understood. We show that the generating series for their generic rank is a rational…

In the first section we study a functor of Bezrukavnikov, Finkelberg and Ostrik defined on character sheaves; we compute it in a Grothendieck group taking weights into account. In the second section we enlarge the class of character sheaves…

Let K_0(V/X) be the relative Grothendieck group of varieties over X in obj(V), with V the category of (quasi-projective) algebraic (resp. compact complex analytic) varieties over a base field k. Then we constructed the motivic Hirzebruch…

We construct a tensor product on Freyd's universal abelian category attached to an additive tensor category or a tensor quiver and establish a universal property. This is used to give an alternative construction for the tensor product on…

We extend the Kechris--Pestov--Todor\v{c}evi\'c correspondence to weak Fra\"{\i}ss\'{e} categories and automorphism groups of generic objects. The new ingredient is the weak Ramsey property. We demonstrate the theory on several examples…

We introduce a notion of $n$-commutativity ($0\le n\le \infty$) for cosimplicial monoids in a symmetric monoidal category ${\bf V}$, where $n=0$ corresponds to just cosimplicial monoids in ${\bf V,}$ while $n=\infty$ corresponds to…

We develop the theory of semi-orthogonal decompositions and spherical functors in the framework of stable $\infty$-categories. Building on this, we study the relative Waldhausen S-construction $S_\bullet(F)$ of a spherical functor $F$ and…

We prove a conjecture by Lusztig, which describes the tensor categories of perverse sheaves on affine flag manifolds, with tensor structure provided by truncated convolution, in terms of the Langlands dual group. We also give a geometric…

In this paper we compute the motivic Chern classes and homology Hirzebruch characteristic classes of (possibly singular) toric varieties, which in the complete case fit nicely with a generalized Hirzebruch-Riemann-Roch theorem. As special…

We study the constant term functor for $\mathbb{F}_p$-sheaves on the affine Grassmannian in characteristic $p$ with respect to a Levi subgroup. Our main result is that the constant term functor induces a tensor functor between categories of…

We construct period sheaves for Hamiltonian spaces, as conjectured in the work of Ben-Zvi, Sakellaridis and Venkatesh, using the perverse pullback functors introduced in the authors' previous work. We prove a dimensional reduction…