# Chow's K/k-image and K/k-trace, and the Lang-Neron theorem

@inproceedings{Conrad2006ChowsKA, title={Chow's K/k-image and K/k-trace, and the Lang-Neron theorem}, author={Brian Conrad}, year={2006} }

Let K/k be an extension of fields, and assume that it is primary: the algebraic closure of k in K is purely inseparable over k. The most interesting case in practice is when K/k is a regular extension: K/k is separable and k is algebraically closed in K. Regularity is automatic if k is perfect. (For K/k finitely generated, regularity is equivalent to K arising as the function field of a smooth and geometrically connected k-scheme.) In the theory of abelian varieties over finitely generated…

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