Abstract
The complete first-order theories of the exponential differential equations of semiabelian varieties are given. It is shown that these theories also arise from an amalgamation-with-predimension construction in the style of Hrushovski. The theories include necessary and sufficient conditions for a system of equations to have a solution. The necessary conditions generalize 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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