Second order linear difference equations over discrete Hardy fields
We shall investigate the properties of solutions of second order linear difference equations defined over a discrete Hardy field via canonical valuations.
Semifields and a theorem of Abhyankar
Abhyankar proved that every field of finite transcendence degree over or over a finite field is a homomorphic image of a subring of the ring of polynomials (for some depending on the field). We conjecture that his result cannot be substantially strengthened and show that our conjecture implies a well-known conjecture on the additive idempotence of semifields that are finitely generated as semirings.
Semi-homomorphisms of near-rings.
Seminearrings, seminearfields and their semigroup-theoretical background.
Semi-normes multiplicatives sur une algèbre de Banach ultramétrique
Separability of the characteristic polynomial
Separating families for semi-algebraic sets.
Separation by hyperplanes in finite-dimensional vector spaces over Archimedean ordered fields.
Severi-Brauer varieties of semidirect product algebras.
Shape tiling.
Sharply Transitive Linear Groups and Nearfields over p-adic Fields.
Signatures et composantes connexes.
Simple zeropotent paramedial groupoids are balanced
This short note is a continuation of and and its purpose is to show that every simple zeropotent paramedial groupoid containing at least three elements is strongly balanced in the sense of .
Simples notes, 1° Sur la limite des racines ; 2° Sur un théorème de Cauchy ; 3° Sur une question de licence
Simples remarques sur les racines entières des équations cubiques
Simples remarques sur les racines entières des équations cubiques
Singularities of analytic functions in a differential ring
Skew fields of noncommutative rational functions (preliminary version)
Skolem–Mahler–Lech type theorems and Picard–Vessiot theory
We show that three problems involving linear difference equations with rational function coefficients are essentially equivalent. The first problem is the generalization of the classical Skolem–Mahler–Lech theorem to rational function coefficients. The second problem is whether or not for a given linear difference equation there exists a Picard–Vessiot extension inside the ring of sequences. The third problem is a certain special case of the dynamical Mordell–Lang conjecture. This allows us to deduce...
Slope filtration of quasi-unipotent overconvergent -isocrystals
We study local properties of quasi-unipotent overconvergent -isocrystals on a curve over a perfect field of positive characteristic . For a --module over the Robba ring , we define the slope filtration for Frobenius structures. We prove that an overconvergent -isocrystal is quasi-unipotent if and only if it has the slope filtration for Frobenius structures locally at every point on the complement of the curve.