Projects per year
Abstract
Zilber’s Exponential Algebraic Closedness conjecture (also known as Zilber’s Nullstellensatz) gives conditions under which a complex algebraic variety should intersect the graph of the exponential map of a semiabelian variety. We prove the special case of the conjecture where the variety has dominant projection to the domain of the exponential map, for abelian varieties and for algebraic tori. Furthermore, in the situation where the intersection is 0dimensional, we exhibit structure in the intersection by parametrizing the sufficiently large points as the images of the period lattice under a (multivalued) analytic map. Our approach is complex geometric, in contrast to a real analytic proof given by Brownawell and Masser just for the case of algebraic tori.
Original language  English 

Pages (fromto)  4046–4081 
Number of pages  36 
Journal  International Mathematics Research Notices 
Volume  2023 
Issue number  5 
Early online date  11 Jan 2022 
DOIs  
Publication status  Published  Mar 2023 
Projects
 1 Finished

Exponentially Algebraically closed fields.
Engineering and Physical Sciences Research Council
1/09/19 → 31/08/22
Project: Research