Research Training Network in Model Theory
Publications > Preprint server > Preprint Number 1346

Preprint Number 1346

Previous Next Preprint server

1346. Alexey Ovchinnikov, Gleb Pogudin and Thomas Scanlon
Effective difference elimination and Nullstellensatz

Submission date: 4 December 2017


We prove effective Nullstellensatz and elimination theorems for difference equations in sequence rings. More precisely, we compute an explicit function of geometric quantities associated to a system of difference equations (and these geometric quantities may themselves be bounded by a function of the number of variables, the order of the equations, and the degrees of the equations) so that for any system of difference equations in variables x = (x_1, ... , x_n) and y = (y_1, ... , y_m), if these equations have any nontrivial consequences in the x variables, then such a consequence may be seen algebraically considering transforms up to the order of our bound. Specializing to the case of n = 0, we obtain an effective method to test whether a given system of difference equations is consistent.

Mathematics Subject Classification:

Keywords and phrases:

Full text arXiv 1712.01412: pdf, ps.

Last updated: December 18 2017 09:24 Please send your corrections to: