The theory of the exponential differential equations of semiabelian varieties

Kirby, J (2009) The theory of the exponential differential equations of semiabelian varieties. Selecta Mathematica, 15 (3). pp. 445-486. ISSN 1022-1824

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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 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.

Item Type: Article
Faculty \ School: Faculty of Science > School of Mathematics
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Depositing User: Users 2731 not found.
Date Deposited: 10 Oct 2011 13:11
Last Modified: 17 Mar 2020 15:45
URI: https://ueaeprints.uea.ac.uk/id/eprint/34969
DOI: 10.1007/s00029-009-0001-7

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