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arXiv · 0708.1352

The theory of the exponential differential equations of semiabelian varieties

Jonathan Kirby
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Abstract

The complete first order theories of the exponential differential equations of semiabelian varieties are given. It is shown that these theories also arises from an amalgamation-with-predimension construction in the style of Hrushovski. The theory includes necessary and sufficient conditions for a system of equations to have a solution. The necessary condition generalizes Ax's differential fields version of Schanuel's conjecture to semiabelian varieties. There is a purely algebraic corollary, the "Weak CIT" for semiabelian varieties, which concerns the intersections of algebraic subgroups with algebraic varieties.

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Jonathan Kirby. 2009-06-09. The theory of the exponential differential equations of semiabelian varieties. https://doi.org/10.1007/s00029-009-0001-7

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