The logic of the product formula

Mardi 31 mai 2016 14:15-15:15 - Ehud Hrushovski - Hebrew University

Résumé : I will discuss the notion of an existentially closed structure, and give classical examples, including the local fields $\mathbbR$, $\mathbbQ_p$, and $k((t))$. I will then describe a language capable of capturing some global structure : roughly, the embedding of a field in its adeles, constrained by the product formula. It is conjectured that $\mathbbQ^a$ and $k((t))^a$ are existentially closed in this language. I will discuss the statement, and a proof in the function field case. There are connections to (distributional) Fekete-Szego theorems, and to non-archimedean Calabi-Yau type theorems. This is joint work with Itaï Ben Yaacov.

Lieu : Bât. 425, salle 117-119

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