Related papers: Endomorphisms of exceptional $D$-elliptic sheaves

We prove that the cohomology rings of the moduli space $M_{d,\chi}$ of one-dimensional sheaves on the projective plane are not isomorphic for general different choices of the Euler characteristics. This stands in contrast to the…

This paper introduces the concept of supermanifolds, viewed as the super-analogues of classical manifolds. Instead of treating supermanifolds as sets of points, we adopt an algebraic-geometric perspective, emphasizing the algebra of…

We construct and study a class of algebras associated to generalized layered graphs, i.e. directed graphs with a ranking function on their vertices. Each finite directed acyclic graph admits countably many structures of a generalized…

We sudy the behaviour of endomorphisms and automorphisms of groups involved in abelian group extensions. The main result can be stated as follows: Let $0\to N\to G\to Q \to 1$ be an abelian group extension. Then one has the following exact…

The aim of this paper is to present elliptic curves defined over function fields of even characteristic having arbitrarily large Mordell-Weil rank. More precisely, we study elliptic curves arising as quartic twist of a supersingular…

We study the endomorphism ring $End(G_A)$ of a subgroup $G_A$ of $\mathbb{Q}^n$ defined by a non-singular $n\times n$-matrix $A$ with integer entries. In the case when the characteristic polynomial of $A$ is irreducible and an extra…

We give a classification of maximal elements of the set of finite groups that can be realized as the automorphism groups of polarized abelian threefolds over finite fields.

We show that compatible systems of $\ell$-adic sheaves on a scheme of finite type over the ring of integers of a local field are compatible along the boundary up to stratification. This extends a theorem of Deligne on curves over a finite…

We introduce the notion of the symplectic characteristic polynomial of an endomorphism of a symplectic vector space. This is a polynomial in two variables and can be considered as a generalization of the characteristic polynomial of the…

Let $X$ be any rational surface. We construct a tilting bundle $T$ on $X$. Moreover, we can choose $T$ in such way that its endomorphism algebra is quasi-hereditary. In particular, the bounded derived category of coherent sheaves on $X$ is…

We give explicit formulas for the number of distinct elliptic curves over a finite field, up to isomorphism, in the families of Legendre, Jacobi, Hessian and generalized Hessian curves.

This is a survey on the automorphism groups in various classes of affine algebraic surfaces and the algebraic group actions on such surfaces. Being infinite-dimensional, these automorphism groups share some important features of algebraic…

We first show that any connected algebraic group over a perfect field is the neutral component of the automorphism group scheme of some normal projective variety. Then we show that very few connected algebraic semigroups can be realized as…

We study the homotopy theory of locally ordered spaces, that is manifolds with boundary whose charts are partially ordered in a compatible way. Their category is not particularly well-behaved with respect to colimits. However, this category…

In this paper we prove an identity in terms of generating functions which enables us to calculate the numbers of isomorphism classes of absolutely indecomposable semistable representations of quivers over finite fields.

We introduce a new class of algebras, which we call cluster-tilted. They are by definition the endomorphism algebras of tilting objects in a cluster category. We show that their representation theory is very close to the representation…

We prove cases of a conjectural rule of H. Yadav, A. Yong, and the author for structure coefficients of the D. Anderson-W. Fulton ring. In particular, we give a combinatorial description for certain localization coefficients of this ring,…

We give an algorithm for computing an inseparable endomorphism of a supersingular elliptic curve $E$ defined over $\mathbb F_{p^2}$, which, conditional on GRH, runs in expected $O(p^{1/2}(\log p)^2(\log\log p)^3)$ bit operations and…

In this note, we consider the $d$-cluster-tilted algebras, the endomorphism algebras of $d$-cluster-tilting objects in $d$-cluster categories. We show that a tilting module over such an algebra lifts to a $d$-cluster-tilting object in this…

This note contains some results related to the definitions of toroidal embeddings and toroidal morphisms over non-closed fields of characteristic zero.