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| Format: | Preprint |
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2024
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| Accès en ligne: | https://arxiv.org/abs/2408.04147 |
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| _version_ | 1866914243348004864 |
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| author | Meretzky, David |
| author_facet | Meretzky, David |
| contents | 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 $1 \to \text{Aut}(M/B) \to \text{Aut}(M/A) \to \text{Aut}(B/A) \to 1$ induces a short exact sequence in definable Galois cohomology. We also discuss compatibilities with [3]. Our result complements the long exact sequence in definable Galois cohomology developed in More on Galois cohomology, definability and differential algebraic groups [4]. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_04147 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The short exact sequence in definable Galois cohomology Meretzky, David Logic 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 $1 \to \text{Aut}(M/B) \to \text{Aut}(M/A) \to \text{Aut}(B/A) \to 1$ induces a short exact sequence in definable Galois cohomology. We also discuss compatibilities with [3]. Our result complements the long exact sequence in definable Galois cohomology developed in More on Galois cohomology, definability and differential algebraic groups [4]. |
| title | The short exact sequence in definable Galois cohomology |
| topic | Logic |
| url | https://arxiv.org/abs/2408.04147 |