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Séminaire Géométrie et théorie des modèles

Horaires : Le vendredi 05 février 2016, 11h

Lieu : ENS, salle W

Pseudo-exponential maps of algebraic groups

Martin Bays (Muenster)

Zilber conjectured that the complex exponential field (C ; + , * , e^x) is quasiminimal - any definable subset is countable or has countable complement. In part as an approach to proving this, Zilber showed how to construct a quasiminimal exponential field (??pseudo-exponentiation?) which is isomorphic to the complex exponential field if Schanuel's conjecture and a certain ??existential closedness? conjecture are true. I will talk on some recent work with Jonathan Kirby exploring variants of this construction. We generalise Zilber's results to exponential maps of other (commutative) algebraic groups, and some related maps, and moreover we show that performing a ??generic? form of the construction allows one to prove quasi-minimality assuming only a substantially weakened form of the existential closedness conjecture, eliminating Schanuel's conjecture entirely.


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