Here we present the algebraic geometry background for the study of PAC fields. The central result is a descent argument which associates to each variety V defined over a finite extension L of a field K a variety W defined over K. Throughout this chapter and subsequent chapters we make the following convention: Whenever we are given a collection of field extensions of a given field K we assume that all of them are contained in a common field.
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© 2008 Springer-Verlag Berlin Heidelberg
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(2008). Elements of Algebraic Geometry. In: Field Arithmetic. Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics, vol 11. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-77270-5_10
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DOI: https://doi.org/10.1007/978-3-540-77270-5_10
Publisher Name: Springer, Berlin, Heidelberg
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