scholarly journals On computable aspects of algebraic and definable closure

2020 ◽  
Author(s):  
Nathanael Ackerman ◽  
Cameron Freer ◽  
Rehana Patel
Keyword(s):  
Algebraic Closure ◽  
Computable Structure

Abstract We investigate the computability of algebraic closure and definable closure with respect to a collection of formulas. We show that for a computable collection of formulas of quantifier rank at most $n$, in any given computable structure, both algebraic and definable closure with respect to that collection are $\varSigma ^0_{n+2}$ sets. We further show that these bounds are tight.

scholarly journals Reynolds stress models of convection in convective cores

2006 ◽  
Vol 2 (S239) ◽  
pp. 77-79 ◽  
Author(s):  
Ian W Roxburgh ◽  
Friedrich Kupka
Keyword(s):  
Reynolds Stress ◽  
Algebraic Closure ◽  
Spherical Geometry ◽  
Turbulent Convection ◽  
Closure Models ◽  
Non Local ◽  
Stress Models

AbstractWe investigate the properties of non-local Reynolds stress models of turbulent convection in a spherical geometry. Regularity at the centre r=0 places constraints on the behaviour of 3rd order moments. Some of the down-gradient and algebraic closure models have inconsistent behaviour at r=0. A combination of down-gradient and algebraic closures gives a consistent prescription that can be used to model convection in stellar cores.

scholarly journals On algebraic closure in pseudofinite fields

2012 ◽  
Vol 77 (4) ◽  
pp. 1057-1066 ◽  
Author(s):  
Özlem Beyarslan ◽  
Ehud Hrushovski
Keyword(s):  
Automorphism Group ◽  
Finite Field ◽  
Algebraic Closure ◽  
Roots Of Unity ◽  
Prime Field ◽  
Almost All ◽  
Pseudofinite Fields

AbstractWe study the automorphism group of the algebraic closure of a substructureAof a pseudo-finite fieldF. We show that the behavior of this group, even whenAis large, depends essentially on the roots of unity inF. For almost all completions of the theory of pseudofinite fields, we show that overA, algebraic closure agrees with definable closure, as soon asAcontains the relative algebraic closure of the prime field.

Link concordance and algebraic closure, II

1989 ◽  
Vol 96 (3) ◽  
pp. 571-592 ◽  
Author(s):  
J. P. Levine
Keyword(s):  
Algebraic Closure ◽  
Link Concordance

scholarly journals GENERALIZED GELFAND–GRAEV REPRESENTATIONS IN SMALL CHARACTERISTICS

2016 ◽  
Vol 224 (1) ◽  
pp. 93-167 ◽  
Author(s):  
JAY TAYLOR
Keyword(s):  
Finite Field ◽  
Wave Front ◽  
Irreducible Character ◽  
Prime Order ◽  
Algebraic Closure ◽  
Characteristic Functions ◽  
Rational Structure ◽  
Reductive Algebraic Group ◽  
Wave Front Set ◽  
Frobenius Endomorphism

Let $\mathbf{G}$ be a connected reductive algebraic group over an algebraic closure $\overline{\mathbb{F}_{p}}$ of the finite field of prime order $p$ and let $F:\mathbf{G}\rightarrow \mathbf{G}$ be a Frobenius endomorphism with $G=\mathbf{G}^{F}$ the corresponding $\mathbb{F}_{q}$-rational structure. One of the strongest links we have between the representation theory of $G$ and the geometry of the unipotent conjugacy classes of $\mathbf{G}$ is a formula, due to Lusztig (Adv. Math. 94(2) (1992), 139–179), which decomposes Kawanaka’s Generalized Gelfand–Graev Representations (GGGRs) in terms of characteristic functions of intersection cohomology complexes defined on the closure of a unipotent class. Unfortunately, the formula given in Lusztig (Adv. Math. 94(2) (1992), 139–179) is only valid under the assumption that $p$ is large enough. In this article, we show that Lusztig’s formula for GGGRs holds under the much milder assumption that $p$ is an acceptable prime for $\mathbf{G}$ ($p$ very good is sufficient but not necessary). As an application we show that every irreducible character of $G$, respectively, character sheaf of $\mathbf{G}$, has a unique wave front set, respectively, unipotent support, whenever $p$ is good for $\mathbf{G}$.

Défaut de semi-stabilité des courbes elliptiques dans le cas non ramifié

2004 ◽  
Vol 56 (4) ◽  
pp. 673-698 ◽  
Author(s):  
Elie Cali
Keyword(s):  
Elliptic Curve ◽  
Algebraic Closure ◽  
Finite Extension ◽  
Good Reduction ◽  
Modular Invariant

AbstractLet be an algebraic closure of ℚ2 and K be an unramified finite extension of ℚ2 included in . Let E be an elliptic curve defined over K with additive reduction over K, and having an integral modular invariant. Let us denote by Knr the maximal unramified extension of K contained in . There exists a smallest finite extension L of Knr over which E has good reduction. We determine in this paper the degree of the extension L/Knr.

scholarly journals Computing -series of geometrically hyperelliptic curves of genus three

2016 ◽  
Vol 19 (A) ◽  
pp. 220-234 ◽  
Author(s):  
David Harvey ◽  
Maike Massierer ◽  
Andrew V. Sutherland
Keyword(s):  
Quadratic Field ◽  
Algebraic Closure ◽  
Zeta Functions ◽  
Hyperelliptic Curves ◽  
Double Cover ◽  
Good Reduction ◽  
Usual Form ◽  
Local Zeta Functions ◽  
Curves Of Genus Three

Let$C/\mathbf{Q}$be a curve of genus three, given as a double cover of a plane conic. Such a curve is hyperelliptic over the algebraic closure of$\mathbf{Q}$, but may not have a hyperelliptic model of the usual form over$\mathbf{Q}$. We describe an algorithm that computes the local zeta functions of$C$at all odd primes of good reduction up to a prescribed bound$N$. The algorithm relies on an adaptation of the ‘accumulating remainder tree’ to matrices with entries in a quadratic field. We report on an implementation and compare its performance to previous algorithms for the ordinary hyperelliptic case.

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