Submission date: 8 August 2024

Abstract:

In Remarks on Galois Cohomology and Definability [2], Pillay introduced definable Galois cohomology, a model-theoretic generalization of Galois cohomology. Let M be an atomic and strongly ω-homogeneous structure over a set of parameters A. Let B be a normal extension of A in M. We show that a short exact sequence of automorphism groups 1 → Aut(M/B) → Aut(M/A) → Aut(B/A) → 1 induces a short exact sequence in definable Galois cohomology. Our result complements the long exact sequence in definable Galois cohomology developed in More on Galois cohomology, definability and differential algebraic groups [3].

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Full text arXiv 2408.04147: pdf, ps.