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An Isaac Newton Institute Workshop

An Introduction to Recent Applications of Model Theory

Nonstandard 1-dimensional tori are locally modular

Authors: Kobi Peterzil (U. Haifa), S. Starchenko ()

Abstract

In earlier work we showed how a uniform family of biholomorphisms of 1-dimensional complex tori and algebraic cubics is definable in $R_{an,exp}$, covering in this way all smooth cubics, but not all tori.

As a corollary, one obtains in elementary extensions of $R_{an,exp}$ some ``nonstandard'' 1-dimensional tori. I will discuss the induced analytic structure on these tori and show that these nonstandard tori are strongly minimal and locally modular.