Weil's Galois Descent Theorem from a computational point of view

Abstract

Let $\mathcal{L}/\mathcal{K}$ be a finite Galois extension and let $X$ be an affine algebraic variety defined over $\mathcal{L}$. Weil's Galois descent theorem provides necessary and sufficient conditions for $X$ to be definable over $\mathcal{K}$, that is, for the existence of an algebraic variety $Y$ defined over $\mathcal{K}$ together with a birational isomorphism $R:X\to Y$ defined over $\mathcal{L}$. Weil's proof does not provide a method to construct the birational isomorphism $R.$ The aim of this paper is to give an explicit construction of $R$.

arXiv comment11 pages

References in corpus (2)

• Fields of moduli of classical Humbert curves
• Field of moduli of generalized Fermat curves

Cited by in corpus (3)

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