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Preprint Number 91
91. Sonia L'Innocente, Angus Macintyre Towards Decidability of the Theory of Pseudo-Finite Dimensional
Representations of sl_2 k; I E-mail: E-mail: Submission date: 17 October 2007 Abstract: We investigate the theory of pseudo-finite dimensional representations of the Lie algebra sl_2 k, where k is an algebraically closed field of characteristic 0. Our principal contribution is to bring out a connection to fundamental problems in the diophantine geometry of curves. We expect to show, in a subsequent paper, that the theory of pseudo-finite dimensional representations of sl_2 k is decidable, modulo some widely believed conjectures in diophantine geometry. Mathematics Subject Classification: 03C60 Keywords and phrases: Pseudo-finite dimensional representations, von Neumann rings, decidable theories. |

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