MORE ON GALOIS COHOMOLOGY, DEFINABILITY AND DIFFERENTIAL ALGEBRAIC GROUPS

Omar Leon Sanchez, David Meretzky, Anand Pillay

Research output: Contribution to journalArticlepeer-review

Abstract

As a continuation of the work of the third author in [5], we make further observations on the features of Galois cohomology in the general model theoretic context. We make explicit the connection between forms of definable groups and first cohomology sets with coefficients in a suitable automorphism group. We then use a method of twisting cohomology (inspired by Serre’s algebraic twisting) to describe arbitrary fibres in cohomology sequences – yielding a useful “finiteness” result on cohomology sets.
Applied to the special case of differential fields and Kolchin’s constrained cohomology, we complete results from [3] by proving that the first constrained cohomology set of a differential algebraic group over a bounded, differentially large, field is countable.
Original languageEnglish
JournalThe Journal of Symbolic Logic
Publication statusAccepted/In press - 2 Apr 2024

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