On elementary equivalence, isomorphism and isogeny of arithmetic function fields
逻辑
2007-05-23 v1 数论
摘要
Motivated by recent work of Florian Pop, we study the connections between three notions of equivalence of function fields: isomorphism, elementary equivalence, and the condition that each of a pair of fields can be embedded in the other, which we call isogeny. Some of our results are purely geometric: we give an isogeny classification of Severi-Brauer varieties and of quadric surfaces. These results are applied to deduce new instances of "elementary equivalence implies isomorphism": for all genus zero curves over a number field, and for certain genus one curves over a number field, including some which are not elliptic curves.
引用
@article{arxiv.math/0406133,
title = {On elementary equivalence, isomorphism and isogeny of arithmetic function fields},
author = {Pete L. Clark},
journal= {arXiv preprint arXiv:math/0406133},
year = {2007}
}
备注
23 pages