Fields of definition of abelian varieties with real multiplication
نویسنده
چکیده
Let K be a field, and let K be a separable closure of K. Let C be an elliptic curve over K. For each g in the Galois group G := Gal(K/K), let C be the elliptic curve obtained by conjugating C by g. One says that C is an elliptic K-curve if all the elliptic curves C are K-isogenous to C. Recall that a subfield L of K is said to be a (2, . . . , 2)-extension of K if L is a compositum of a finite number of quadratic extensions of K in K. The extension L/K is then Galois, and Gal(L/K) is an elementary abelian 2-group. Recently, N. Elkies proved:
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