... PAUL VOJTA §2. Conventions and required knowledge in algebraic geometry It is assumed that the reader is familiar with the basics of algebraic geometry as given, e.g., in the first three chapters of =-=[H]-=-, especially the first two. Note, however, that some conventions are different here. This book will primarily use the language of schemes, rather than of varieties. The reader who prefers the more ele...

...and the images of X1, . . . , Xn . Then k ′ is a purely inseparable extension of the algebraic closure of k in K ; moreover, K is separable over k if and only if k ′ is separable over k . Proof. See (=-=[W]-=-, Ch. 1, Prop. 23). Corollary 3.14. Let X be a variety over a field k , and let k ′ be the minimal field of definition of X . Then k ′ is a purely inseparable extension of the algebraic closure of k i...