Embedding stable groups into algebraic groups

2025/10/28 by Bartnick, Charlotte
#FOS: Mathematics #Logic (math.LO)

paper · doi:10.48550/arxiv.2510.24504

Abstract

Adapting a proof of Bouscaren and Delon, we show that every type-definable connected group in a given stable theory of fields embeds into an algebraic group, under a condition on the definable closure. We also present general hypotheses which yield a uniform description of the definable closure in such theories of fields. The setting includes in particular the theories of separably closed fields of arbitrary degree of imperfection and differentially closed fields of arbitrary characteristic.

Citations

• On groups definable in geometric fields with generic derivations
• Neostability transfers in derivation-like theories
• Stationarity and elimination of imaginaries in stable and simple theories
• Separably differentially closed fields
• Model theory of derivations of the Frobenius map revisited
• De Beaux Groupes
• Model theory of fields with free operators in characteristic zero

Related

• A short note on groups in separably closed valued Fields
• Definable Groups in DCFA
• Groups interpretable in theories of fields
• Stationarity and elimination of imaginaries in stable and simple theories
• On definable groups in real closed fields with a generic derivation, and related structures