We study algebraic and model-theoretic properties of existentially closed fields with an
action of a fixed finite group. Such fields turn out to be pseudo-algebraically closed in a …

We give algebraic conditions for a finite commutative algebra $ B $ over a field of positive
characteristic, which are equivalent to the companionability of the theory of fields with “$ B …

We study integrating (that is expanding to a Hasse–Schmidt derivation) derivations, and
more generally truncated Hasse–Schmidt derivations, satisfying iterativity conditions given …

For a group G, we define the notion of a G‐kernel and show that the properties of G‐kernels
are closely related with the existence of a model companion of the theory of Galois actions of …

On Hasse–Schmidt Derivations: The Action of Substitution Maps | SpringerLink Skip to main
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We show that the theory of Galois actions of a torsion Abelian group A is companionable if
and only if, for each prime p, the p-primary part of A is either finite or it coincides with the …

Let k be a commutative ring and A a commutative k-algebra. In this paper we introduce the
notion of enveloping algebra of Hasse–Schmidt derivations of A over k and we prove that …

Nous donnons une preuve alternative, valable en toute caractéristique, d'un ancien résultat
de Lascar caractérisant les automorphismes bornés d'un corps algébriquement clos. Cette …

We study model theory of fields with actions of a fixed finite group scheme. We prove the
existence and simplicity of a model companion of the theory of such actions, which …

ISOSINGULARITY, DIFFERENTIALITY, AND NON-TRIVIAL ANALYTIC FACTORS OF
ALGEBRAIC SINGULARITIES Page 1 HAL Id: hal-04439326 https://hal.science/hal-04439326 …