Related papers: Generalized Albanese and its dual
We consider the category of Deligne 1-motives over a perfect field k of exponential characteristic p and its derived category for a suitable exact structure after inverting p. As a first result, we provide a fully faithful embedding into an…
We introduce the universal unitarily graded A-algebra for a commutative ring A and an arbitrary abelian extension U of the group of units of A, and use this concept to give simplified proofs of the main theorems of co-Galois theory in the…
Categorical universal algebra can be developed either using Lawvere theories (single-sorted finite product theories) or using monads, and the category of Lawvere theories is equivalent to the category of finitary monads on Set. We show how…
In the present paper, we prove the existence of universal polynomials which express multi-singularity loci classes of prescribed types for proper morphisms between smooth schemes over an algebraically closed field of characteristic zero --…
If k is an arbitrary field, we construct a category of k-1-motives in which every commutative algebraic k-group G has a dual object $G^{\vee}$. When k is a local field of arbitrary characteristic, we establish Pontryagin duality theorems…
Let U be a smooth quasi-projective variety over a field k that is finite, the algebraic closure of a finite field or algebraically closed of characteristic 0. Let X be a suitable projective compactification of U, and D an effective divisor…
We study the universal cover of the complex one-dimensional torus as a model-theoretic structure in a natural language. We consider also abstract covers of one-dimensional tori over algebraically closed fields of characteristic zero. The…
We continue our study on smooth complex projective varieties $X$ of maximal Albanese dimension and of general type satisfying $\chi(X, \omega_X)=0$. We formulate a conjectural characterization of such varieties and prove this conjecture…
We consider finitely generated normal algebras over an algebraically closed field of characteristic zero that come with a complexity one grading by a finitely generated abelian group such that the conditions of a UFD are satisfied for…
Let $k$ be an algebraically closed field of characteristic $p>0$. We give a birational characterization of ordinary abelian varieties over $k$: a smooth projective variety $X$ is birational to an ordinary abelian variety if and only if…
We develop the theory of difference algebraic groups in the case where we have finitely many pairwise commuting difference operators. We show that the defining ideal of a difference algebraic group is finitely generated as a difference…
It is an important aspect of cluster theory that cluster categories are "categorifications" of cluster algebras. This is expressed formally by the (original) Caldero-Chapoton map X which sends certain objects of cluster categories to…
We introduce the notion of universal odd generalized Poisson superalgebra associated to an associative algebra A, by generalizing a construction made in [5]. By making use of this notion we give a complete classification of simple linearly…
One develops {\em ab initio} the theory of rational/birational maps over reduced, but not necessarily irreducible, projective varieties in arbitrary characteristic. A numerical invariant of a rational map is introduced, called the Jacobian…
We expand our previously founded basic theory of equiresidual algebraic geometry over an arbitrary commutative field, to a well-behaved theory of (equiresidual) algebraic varieties over a commutative field, thanks to the generalisation of…
We study the birational geometry of varieties of maximal Albanese dimension. In particular we discuss criteria for a generically finite morphism of varieties of maximal Albanese dimension to be birational; we give a new characterization of…
Universal algebra uniformly captures various algebraic structures, by expressing them as equational theories or abstract clones. The ubiquity of algebraic structures in mathematics and related fields has given rise to several variants of…
We classify all rational maps $H \in K(x)^n$ for which ${\rm trdeg}_K K(tH_1,tH_2,\ldots,tH_n) \le 2$, where $K$ is any field and $t$ is another indeterminate. Furthermore, we classify all such maps for which additionally $JH \cdot H = {\rm…
We classify Galois objects for the dual of a group algebra of a finite group over an arbitrary field.
The purpose of this contribution is to give a coherent account of a particular narrative which links locales, geometric theories, sheaf semantics and constructive commutative algebra. We are hoping to convey a firm grasp of three ideas: (1)…