The theory of the exponential differential equations of semiabelian varieties

Kirby, J ORCID: https://orcid.org/0000-0003-4031-9107 (2009) The theory of the exponential differential equations of semiabelian varieties. Selecta Mathematica-New Series, 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 (former - to 2024)
UEA Research Groups:	Faculty of Science > Research Groups > Logic (former - to 2024) Faculty of Science > Research Groups > Algebra, Logic & Number Theory
Depositing User:	Users 2731 not found.
Date Deposited:	10 Oct 2011 13:11
Last Modified:	07 Nov 2024 12:33
URI:	https://ueaeprints.uea.ac.uk/id/eprint/34969
DOI:	10.1007/s00029-009-0001-7

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