相关论文: Images of abelian schemes

We prove a purity theorem for abelian schemes in arbitrary unramified mixed characteristic (0,p). The case p=2 is completely new and the case p>2 fixes several errors in the literature.

In this paper we will obtain some further properties for specializations in a scheme. Using these results, we will take a picture for a scheme and a picture for a morphism of schemes. In particular, we will prove that every morphism of…

We give criteria for certain morphisms from an algebraic stack to a (not necessarily algebraic) stack to admit an (appropriately defined) scheme-theoretic image. We apply our criteria to show that certain natural moduli stacks of local…

We give a necessary and sufficient condition for a morphism between recollements of abelian categories to be an equivalence.

We study in this paper some criterions to get polarized morphisms between abelian varieties. We deduce explicit dynamical systems with particular intersection properties.

We study the interaction between the group law on an abelian variety and the additive structure induced on its image under a morphism to projective space. Let $A/F$ be a simple abelian variety, $f:A \rightarrow \mathbb{P}^n$ be a morphism…

A comma category, exemplified in algebraic geometry by coherent systems, combines two categories over a third through morphisms between their objects. We establish sufficient conditions for it to be abelian, compute its Grothendieck group,…

Relations between some kinds of formal and standard smoothness, for morphisms of schemes, are clarified in surprisingly simple and direct ways, bypassing much of the customarily employed machinery. Even the deep local-to-global property of…

Let $A$ be an abelian variety over an algebraically closed field. We show that $A$ is the automorphism group scheme of some smooth projective variety if and only if $A$ has only finitely many automorphisms as an algebraic group. This…

This paper shows some criteria for a scheme of finite type over an algebraically closed field to be non-singular in terms of jet schemes. For the base field of characteristic zero, the scheme is non-singular if and only if one of the…

An association scheme is called amorphic if every possible fusion of relations gives rise to a fusion scheme. We call a pair of relations fusing if fusing that pair gives rise to a fusion scheme. We define the fusing-relations graph on the…

Motivated by the work of Esnault-Hai, one has the notion of de Rham $K(\pi,1)$ schemes, defined as follows. Given a smooth proper geometrically connected scheme $X$ over a field $k$ of characteristic 0 and a base point $x \in X (k)$, one…

In this paper we provide sufficient conditions in order to show that the set image of a continuous and shift-commuting map defined on a shift space over an arbitrary discrete alphabet is also a shift space; additionally, if such a map is…

We show that a given set of first class constraints becomes abelian if one maps each constraint to the surface of other constraints. There is no assumption that first class constraints satisfy a closed algebra. The explicit form of the…

Let $u:A\to B$ be a morphism of noetherian local rings. We obtain smoothness criteria for algebras with differential bases, in the case of rings containing a field of characteristic $p>0.$ We also give smoothness criteria for reduced…

Necessary and sufficient conditions for the exactness (in the algebraic sense) of certain sequences of continuous group homomorphisms are established.

We give a criterion for a group homomorphism on a valued abelian group to be surjective and to preserve spherical completeness. We apply this to give a criterion for the existence of integration on a valued differential field. Further, we…

We show that on an Abelian variety over an algebraically closed field of positive characteristic, the obstruction to lifting an automorphism to an Abelian variety over a field of characteristic zero as a morphism vanishes if and only if it…

We study topological group theoretic properties of algebraic groups over local fields. In particular, we find conditions under which such groups have closed images under arbitrary continuous homomorphisms into arbitrary topological groups.

We obtain conditions on the Lee form under which a holomorphic map between almost Hermitian manifolds is a harmonic map or morphism. Then we discuss under what conditions (i) the image of a holomorphic map from a cosymplectic manifold is…