Work

On groups definable in geometric fields with generic derivations

Year: 2026

Type: article

Abstract: We study groups definable in existentially closed geometric fields with commuting derivations. Our main result is that such a group can be definably embedded in a group interpretable in the underlying geometric field. Compared to earlier work of the first two authors toguether with K. Peterzil, the novelty is that we also deal with infinite dimensional groups.

Source: Proceedings of the American Mathematical Society

DOI: 10.1090/proc/17805

Authors: Anand Pillay, Françoise Point, Silvain Rideau-Kikuchi

Institutions: Centre National de la Recherche Scientifique, Université Paris Sciences et Lettres, École Normale Supérieure - PSL, Département de mathématiques et applications

Language: English

Topic: Advanced Topology and Set Theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: National Science Foundation, Deutsche Forschungsgemeinschaft, Agence Nationale de la Recherche

Awards: Topics in Model Theory, G3821848849, MFAI: Logic and the Theory of Neural Language Models