Related papers: A Sheaf Model of the Algebraic Closure

Let X be an affine real algebraic set . We investigate on the theory of algebraically constructible functions on X and the description of the semi-algebraic subsets of X when we replace the polynomial functions on X by some rational…

We show how to build models of Synthetic Algebraic Geometry over rings k such that finitely presented k-algebra have a decidable equality. The construction is done in a constructive and weak (same proof theoretic strength as dependent type…

Computational content encoded into constructive type theory proofs can be used to make computing experiments over concrete data structures. In this paper, we explore this possibility when working in Coq with chain complexes of infinite type…

Let $S$ be a unital associative ring and $S[t;\sigma,\delta]$ be a skew polynomial ring, where $\sigma$ is an injective endomorphism of $S$ and $\delta$ a left $\sigma$-derivation. For each $f\in S[t;\sigma,\delta]$ of degree $m>1$ with a…

We study the automorphism group of the algebraic closure of a substructure A of a pseudo-finite field F. We show that the behavior of this group, even when A is large, depends essentially on the roots of unity in F. For almost all…

We introduce a notion of constructibility for \'etale sheaves with torsion coefficients over a suitable class of adic spaces. This notion is related to the classical notion of constructibility for schemes via the nearby cycles functor. We…

We give an algorithm for constructing the algebraic hull of a given matrix Lie algebra in characteristic zero. It is based on an algorithm for finding integral linear dependencies of the roots of a polynomial, that is probably of…

We study rational Cherednik algebras over an algebraically closed field of positive characteristic. We first prove several general results about category O, and then focus on rational Cherednik algebras associated to the general and special…

In this short note, we will show the following weak evidence of S. Lang conjecture over function fields. Let f : X ---> Y be a projective and surjective morphism of algebraic varieties over an algebraically closed field k of characteristic…

We compare some algebras appeared in the recent attempts to prove resolution of singularities in positive characteristic. We also construct an algebra which encodes the same information and it is equivalent, up to integral closure, to the…

A basic finite dimensional algebra over an algebraically closed field $k$ is isomorphic to a quotient of a tensor algebra by an admissible ideal. The category of left modules over the algebra is isomorphic to the category of representations…

We provide an internal characterization of those finite algebras (i.e., algebraic structures) $\mathbf A$ such that the number of homomorphisms from any finite algebra $\mathbf X$ to $\mathbf A$ is bounded from above by a polynomial in the…

Let K be an algebraically closed field of characteristic zero, endowed with a complete nonarchimedean norm. Let X be a K-rigid analytic variety and \Sigma a semianalytic subset of X. Then the closure of \Sigma in X with respect to the…

Alternating bilinear maps with few relations allow to define a combinatorial closure similarly as in [2]. For the $\aleph_0$-categorical case we show that this closure is part of the algebraic closure.

We prove a microlocal characterisation of character sheaves on a reductive Lie algebra over an algebraically closed field of sufficiently large positive characteristic: a perverse irreducible G-equivariant sheaf is a character sheaf if and…

Let $f$ be a polynomial in the free algebra over a field $K$, and let $A$ be a $K$-algebra. We denote by $\S_A(f)$, $\A_A(f)$ and $\I_A(f)$, respectively, the `verbal' subspace, subalgebra, and ideal, in $A$, generated by the set of all…

We study quadratic Lie algebras over a field K of null characteristic which admit, at the same time, a symplectic structure. We see that if K is algebraically closed every such Lie algebra may be constructed as the T*-extension of a…

A computably presented algebraic field $F$ has a \emph{splitting algorithm} if it is decidable which polynomials in $F[X]$ are irreducible there. We prove that such a field is computably categorical iff it is decidable which pairs of…

We prove that any geometrically connected curve $X$ over a field $k$ is an algebraic $K(\pi,1)$, as soon as its geometric irreducible components have nonzero genus. This means that the cohomology of any locally constant constructible…

A deductive system is structurally complete if its admissible inference rules are derivable. For several important systems, like modal logic S5, failure of structural completeness is caused only by the underivability of passive rules, i.e.…