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arXiv · 1707.08171

Locally C-Nash groups

Elías Baro·Juan de Vicente·Margarita Otero
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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).

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Elías Baro, Juan de Vicente, Margarita Otero. 2018-09-10. Locally C-Nash groups. https://doi.org/10.1007/s13163-018-0278-1

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