Locally C-Nash groups
Abstract
We introduce the category of locally C-Nash groups, basic examples of such groups are complex algebraic groups. We prove that if two complex algebraic groups are locally C-Nash isomorphic then they also are biregularly isomorphic. We also show that both, abelian locally Nash and abelian locally C-Nash groups, can be characterized via meromorphic maps admitting an algebraic addition theorem; we give an invariant of such groups associated to the groups of periods of a chart at the identity. Finally, we prove that the category of simply connected abelian locally C-Nash groups coincides with that of universal coverings of the abelian complex irreducible algebraic groups (a complex version of a result of Hrushovski and Pillay).
Cite
@article{arxiv.1707.08171,
title = {Locally C-Nash groups},
author = {Elías Baro and Juan de Vicente and Margarita Otero},
journal= {arXiv preprint arXiv:1707.08171},
year = {2018}
}
Comments
25 pages. arXiv admin note: text overlap with arXiv:1506.00405. To appear in Revista Matem\'atica Complutense