Related papers: A decisive Theorem (Un th\'eor\`eme d\'ecisif)

We prove that the number of parameters defining a complex of projective modules over a finite dimensional algebra is upper semi-continuous in families of algebras. Supposing that every algebra is either derived tame or derived wild, we get…

A commutative order in a quaternion algebra is called selective if it is embeds into some, but not all, the maximal orders in the algebra. It is known that a given quadratic order over a number field can be selective in at most one…

In this note we prove that every non characteristically filiform Lie algebra is endowed with an affine structure.

We prove that in a countable theory T fully stable over a predicate P, any complete set A has the existence property. This means that A can be extended to a model of T without changing the P-part. In particular, T has the Gaifman property:…

If V is a finitely generated variety such that the first-order theory of the finite members of V is decidable, we show that V is residually finite, and in fact has a finite bound on the sizes of subdirectly irreducible algebras. This result…

Let $X$ be a variety over a complete nontrivially valued field $K$. We construct an algebraizable formal model for the analytification of $X$ in the case $X$ admits a closed embedding into a toric variety. By algebraizable we mean that the…

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 study the representation theory of finite-dimensional $\omega$-Lie algebras over the complex field. We derive an $\omega$-Lie version of the classical Lie's theorem, i.e., any finite-dimensional irreducible module of a soluble…

We show, under some natural conditions, that the set of abelian points on the non-anomalous subset of a closed irreducible subvariety $X$ intersected with the union of connected algebraic subgroups of codimension at least $\dim X$ in a…

Let $R$ be a complete discrete valuation ring with fraction field $K$ and with algebraically closed residue field. Let $X$ be a faithfully flat $R$-scheme of finite type of relative dimension 1 and $G$ be any affine $K$-group scheme of…

An abelian variety over a field K is said to have big monodromy, if the image of the Galois representation on l-torsion points, for almost all primes l contains the full symplectic group. We prove that all abelian varieties over a finitely…

The main result of this paper is that every (separated) toric variety which has a semigroup structure compatible with multiplication on the underlying torus is necessarily affine. In the course of proving this statement, we also give a…

The purpose of this paper is to give an elementary proof to the theorem due to Avramov on certain determinantal ideals of linear type.

Rice's theorem shows that nontrivial extensional properties of partial recursive functions are undecidable. For finite weighted Boolean optimization/CSP-style slices, a Rice-style structural analogue holds for tractability classification:…

Every nontrivial abelian variety over a Hilbertian field in which the weak Mordell-Weil theorem holds admits infinitely many torsors with period any $n > 1$ which is not divisible by the characteristic. The corresponding statement with…

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 show that varieties of dimension at least 2 over infinite fields are determined as abstract schemes by their Zariski topological spaces together with the rational equivalence relation on the set of effective divisors. This gives a…

An \'etale structure over a topological space $X$ is a continuous family of structures (in some first-order language) indexed over $X$. We give an exposition of this fundamental concept from sheaf theory and its relevance to countable model…

In this paper we study the behaviour of modules over finite dimensional algebras whose endomorphism algebra is a division ring. We show that there are finitely many such modules in the module category of an algebra if and only if the length…

We study a well-known technique of using absoluteness for giving choice-free proofs to some statements which are known to be provable with the axiom of choice. The idea is to reduce the problem to an inner model where the axiom of choice…