相关论文: The Grothendieck and Picard groups of a complete t…

We introduce the notion of a matroid M over a commutative ring R, assigning to every subset of the ground set an R-module according to some axioms. When R is a field, we recover matroids. When R=$\mathbb{Z}$, and when R is a DVR, we get…

Building up on work of Epstein, May and Drury, we define and investigate the mod $p$ Steenrod operations on the de Rham cohomology of smooth algebraic stacks over a field of characteristic $p>0$. We then compute the action of the operations…

Let X be a smooth projective variety with the action of the n dimensional torus. The article describes the moduli space of torus equivariant morphisms from stable toric varieties into X as the inverse limit of the GIT quotients of X and…

We calculate the Picard group, over the integers, of the Hilbert scheme of smooth, irreducible, non-degenerate curves of degree $d$and genus $g \geq 4$ in ${\Bbb P}^r$, in the case when $d \geq 2g+1 $ and $r \leq d-g$. We express the…

We prove that the automorphism group of a toric Deligne-Mumford stack is isomorphic to the $2$-group associated to the stacky fan.

We establish a Hirzebruch-Riemann-Roch type theorem and Grothendieck-Riemann-Roch type theorem for matrix factorizations on quotient Deligne-Mumford stacks. For this we first construct a Hochschild-Kostant-Rosenberg type isomorphism…

In this paper, we use $\mathcal D$-split sequences and derived equivalences to provide formulas for calculation of higher algebraic $K$-groups (or mod-$p$ $K$-groups) of certain matrix subrings which cover tiled orders, rings related to…

Families of stable curves of genus $\gamma$ over a smooth curve $C$ correspond to morphisms from $C$ to the moduli stack of stable curves $\bar{\cal M}_\gamma$. It is natural to compactify the corresponding moduli problem using stable maps…

For every smooth and separated Deligne-Mumford stack $F$, we associate a motive $M(F)$ in Voevodsky's category of mixed motives with rational coefficients $\mathbf{DM}^{\eff}(k,\mathbb{Q})$. When $F$ is proper over a field of characteristic…

We present a new compactification $M(d,n)$ of the moduli space of self-maps of $\mathbb{CP}^1$ of degree $d$ with $n$ markings. It is constructed via GIT from the stable maps moduli space $\ ar M_{0,n}(\mathbb{CP}^1 \times \mathbb{CP}^1,…

Let K 0 (Fp GLn(Fp)-proj) denote the Grothendieck group of finitely generated pro-jective Fp GLn(Fp)-modules. We show that the algebra C $\otimes$ n$\ge$0 K 0 (Fp GLn(Fp)-proj) with multiplication given by induction functors, is a…

Let $X$ be a smooth projective curve over the complex numbers. We compute the Brauer group of the moduli stack of Bruhat-Tits group scheme $\mathcal{G}$-torsors on $X$. When $g(X) \geq 3$ we compute the Brauer group of the regularly stable…

We compute the class of the classifying stack of the exceptional algebraic group $G_2$ and of the spin groups $\mathrm{Spin}_7$ and $\mathrm{Spin}_8$ in the Grothendieck ring of stacks, and show that they are equal to the inverse of the…

In this paper, which is a sequel of arXiv:2002.07494, we investigate, for any reductive group $G$ over an algebraically closed field $k$, the Picard group of the universal moduli stack $\mathrm{Bun}_{G,g,n}$ of $G$-bundles over $n$-pointed…

We study dualizing complexes on algebraic stacks. In particular, we show their existence for (tame) Deligne--Mumford stacks of equicharacteristic in great generality.

In this paper we study the topology of the stack $\mathcal{T}_g$ of smooth trigonal curves of genus g, over the complex field. We make use of a construction by the first named author and Vistoli, that describes $\mathcal{T}_g$ as a quotient…

The goal of this paper is to prove Riemann-Roch type theorems for Deligne-Mumford algebraic stacks. To this end, we introduce a "cohomology with coefficients in representations" and a Chern character, and we prove a…

Given a smooth scheme X with an action by an affine algebraic group G, we give a formula to compute the Nisnevich sheaf of the motivic connected components of the quotient stack [X/G] in the case of an orbifold. We apply it to identify all…

Let $k$ be an algebraically closed field of characteristic zero, and let $\mathcal{C} = \mathcal{R}-mod$ be the category of finite-dimensional modules over a fixed Hopf algebra over $k$. One may form the wreath product categories…

We construct relative moduli spaces of semistable pairs on a family of projective Deligne-Mumford stacks. We define moduli stacks of stable orbifold Pandharipande-Thomas pairs on stacks of expanded degenerations and pairs, and then show…