相关论文: Specialization of N\'eron-Severi groups in positiv…

A classical result in complex geometry says that the automorphism group of a manifold of general type is discrete. It is more generally true that there are only finitely many surjective morphisms between two fixed projective manifolds of…

We propose a conjectural extension to positive characteristic case of a well known Deligne's theorem on the existence of super fiber functors. We prove our conjecture in the special case of semisimple categories with finitely many…

Motivated by Lang-Vojta's conjecture, we show that the set of dominant rational self-maps of an algebraic variety over a number field with only finitely many rational points in any given number field is finite by combining Amerik's theorem…

We prove a finiteness result for dominant rational maps whose orbifold base is of general type. Our finiteness result generalizes Maehara's theorem that a given variety dominates only finitely many projective varieties of general type up to…

Let $X$ be a normal projective variety and $f:X\to X$ a non-isomorphic polarized endomorphism. We give two characterizations for $X$ to be a toric variety. First we show that if $X$ is $\mathbb{Q}$-factorial and $G$-almost homogeneous for…

In this note we prove a variational open adelic image theorem for the Galois action on the cohomology of smooth proper $S$-schemes where $S$ is a smooth variety over a finitely generated field of positive characteristic. A central tool is a…

The Shafarevich conjecture/problem is about the finiteness of isomorphism classes of a family of varieties defined over a number field with good reduction outside a finite collection of places. For K3 surfaces, such a finiteness result was…

We consider the rigid monoidal category of character sheaves on a smooth commutative group scheme $G$ over a finite field $k$ and expand the scope of the function-sheaf dictionary from connected commutative algebraic groups to this setting.…

We define Symplectic cohomology groups for a class of symplectic fibrations with closed symplectic base and convex at infinity fiber. The crucial geometric assumption on the fibration is a negativity property reminiscent of negative…

We study the elliptic curve E given by y^2=x(x+1)(x+t) over the rational function field k(t) and its extensions K_d=k(\mu_d,t^{1/d}). When k is finite of characteristic p and d=p^f+1, we write down explicit points on E and show by…

We consider a filtration on the cohomology of the structure sheaf indexed by (not necessarily reduced) divisors ``at infinity''. We show that the filtered pieces have transfers morphisms, fpqc descent, and are so called cube invariant. In…

This work is motivated by the papers [EG85] and [Ngu15] in which the following two problems are solved. Let $\mathcal{O}$ is a finitely generated $\mathbb{Z}$-algebra that is an integrally closed domain of characteristic zero, consider the…

We prove that every geometrically reduced projective variety of pure dimension n over a field of positive characteristic admits a morphism to projective n-space, etale away from the hyperplane H at infinity, which maps a chosen divisor into…

We obtain a criterion for the automorphism group of an affine toric variety to be connected in combinatorial terms and in terms of the divisor class group of the variety. The component group of the automorphism group of a non-degenerate…

The homological conjectures, which date back to Peskine, Szpiro and Hochster in the late sixties, make fundamental predictions about syzygies and intersection problems in commutative algebra. They were settled long ago in the presence of a…

Let $X$ be a smooth projective variety over a perfect field $k$ of characteristic $p>0$, and $V$ be a vector bundle over $X$. It is well known that if $X$ is a curve and $V$ is not strongly semistable, then some Frobenius pullback…

Let $X$ be a smooth proper variety over an algebraically closed field of positive characteristic $p$. We find cohomological conditions for the Artin-Mazur formal group functors $\Phi^{i}(X,\mathbb{G}_m)$ to be formally smooth. We show that…

Let $f : X \rightarrow Y$ be a generically smooth nonconstant morphism between irreducible projective curves, defined over an algebraically closed field, which is \'etale on an open subset of $Y$ that contains both the singular locus of $Y$…

It is shown that a finitely generated branch group has Serre's property (FA) if and only if it does not surject onto the infinite cyclic group or the infinite dihedral group. An example of a finitely generated self-similar branch group…

The Tate conjecture for divisors on varieties over number fields is equivalent to finiteness of $\ell$-primary torsion in the Brauer group. We show that this finiteness is actually uniform in one-dimensional families for varieties that…