Related papers: On Euler Characteristic of equivariant sheaves

Algebraic actions of unipotent groups $U$ actions on affine $k-$varieties $X$ ($k$ an algebraically closed field of characteristic 0) for which the algebraic quotient $X//U$ has small dimension are considered$.$ In case $X$ is factorial,…

We prove a conjecture of Lusztig on a microlocal characterization of his perverse sheaves. For any finite quiver without loops, an equivariant simple perverse sheaf on the variety of quiver representations is a Lusztig's perverse sheaf if…

We study equivariant Arakelov-Euler characteristics of hermitian sheaves on arithmetic varieties which support a tame action by a finite group G. The tameness of the group action allows us to produce an equivariant Arakelov-Euler…

We define a Weil-\'etale complex with compact support for duals (in the sense of the Bloch dualizing cycles complex $\mathbb{Z}^c$) of a large class of $\mathbb{Z}$-constructible sheaves on an integral $1$-dimensional proper arithmetic…

Let X be an algebraic projective variety in {\bf P}^n. Denote by {\cal C}_{\lambda} the space of all effective cycles on X whose homology class is \lambda \in H_{2p} (X,{\bf Z}). It is easy to show that {\cal C}_{\lambda} is an algebraic…

Let $Q$ be a quiver, $M$ a representation of $Q$ with an ordered basis $\cB$ and $\ue$ a dimension vector for $Q$. In this note we extend the methods of \cite{L12} to establish Schubert decompositions of quiver Grassmannians $\Gr_\ue(M)$…

A well-known theorem of W. Fischer and H. Grauert states that analytic fiber spaces with all fibers isomorphic to a fixed compact connected complex manifold are locally trivial. Motivated by this result, we show that if $k$ is an…

Generalizing the star graphs of M\"uller-Stach and Westrich, we describe a class of graphs whose associated graph hypersurface is equipped with a non-trivial torus action. For such graphs, we show that the Euler characteristic of the…

We prove that a finite-dimensional irreducible Hopf algebra $H$ in positive characteristic is semisimple, if and only if it is commutative and semisimple, if and only if the restricted Lie algebra $P(H)$ of the primitives is a torus. This…

Let X be a smooth proper variety over the quotient field of a Henselian discrete valuation ring with algebraically closed residue field of characteristic p. We show that for any coherent sheaf E on X, the index of X divides the…

We prove an analogue of the Riemann-Hurwitz theorem for computing Euler characteristics of pullbacks of coherent sheaves through finite maps of smooth projective varieties, subject only to the condition that the irreducible components of…

For certain tame abelian covers of arithmetic surfaces X/Y we obtain striking formulas, involving a quadratic form derived from intersection numbers, for the equivariant Euler characteristics of both the canonical sheaf !X/Y and also its…

It was proved by Ginzburg and Mirkovic-Vilonen that the $G(O)$-equivariant perverse sheaves on the affine grassmannian of a connected reductive group $G$ form a tensor category equivalent to the tensor category of finite dimensional…

We compute the Euler characteristics of quiver Grassmannians and quiver flag varieties of tree and band modules and prove their positivity. This generalizes some results by G.C. Irelli [arXiv:0910.2592]. As an application we consider the…

Let A be an abelian variety defined over a number field k and let F be a finite Galois extension of k. Let p be a prime number. Then under certain not-too-stringent conditions on A and F we compute explicitly the algebraic part of the…

We prove that for any prime $\ell$, any finite group has as many irreducible complex characters of degree prime to $\ell$ as the normalizers of its Sylow $\ell$-subgroups. This equality was conjectured by John McKay. The conjecture was…

We resolve the Grothendieck-Serre question over an arbitrary base field $k$: for a smooth $k$-group scheme $G$ and a smooth $k$-variety $X$, we show that every generically trivial $G$-torsor over $X$ trivializes Zariski semilocally on $X$.…

Let $G$ be a complex, connected, reductive, algebraic group, and $\chi:\mathbb{C}^\times \to G$ be a fixed cocharacter that defines a grading on $\mathfrak{g}$, the Lie algebra of $G$. Let $G_0$ be the centralizer of…

We introduce a class of perverse sheaves on a partial flag manifold of a connected reductive group G defined over a finite field which are equivariant under the action of the group of rational points of G. The definition of this class is…

Olsson showed in [Ols25] that if $\mathcal{X} \to X$ is a $\mathbf{G}_m$-gerbe over a smooth projective variety over an algebraically closed field $k$ such that the Brauer class of $\mathcal{X}$ has order prime to the characteristic of $k$,…