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• W3143206344 abstract "A theorem of Elekes and Szabo recognizes algebraic groups among certain complex algebraic varieties with maximal size intersections with finite grids. We establish a generalization to relations of any arity and dimension, definable in: 1) stable structures with distal expansions (includes algebraically and differentially closed fields of characteristic 0); and 2) o-minimal expansions of groups. Our methods provide explicit bounds on the power saving exponent in the non-group case. Ingredients of the proof include: a higher arity generalization of the abelian group configuration theorem in stable structures, along with a purely combinatorial variant characterizing Latin hypercubes that arise from abelian groups; and Zarankiewicz-style bounds for hypergraphs definable in distal structures." @default.
• W3143206344 created "2021-04-13" @default.
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• W3143206344 creator A5084285139 @default.
• W3143206344 date "2021-04-06" @default.
• W3143206344 modified "2023-10-16" @default.
• W3143206344 title "Model-theoretic Elekes-Szab'o for stable and o-minimal hypergraphs" @default.
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