Real Hypersurfaces Contained in Abelian Varieties

Real abelian varieties with complex multiplication

Abelian Varieties

This the original TEX file for my article Abelian Varieties, published as Chapter V of Arithmetic geometry (Storrs, Conn., 1984), 103–150, Springer, New York, 1986. The table of contents has been restored, some corrections have been made,1 there are minor improvements to the exposition, and an index has been added. The numbering is unchanged.

The distance between superspecial abelian varieties with real multiplication

Article history: Received 17 June 2008 Communicated by B. Conrad MSC: primary 14K02 secondary 11E10

Fields of definition of abelian varieties with real multiplication

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 ...

Generic Abelian Varieties with Real Multiplication Are Not Jacobians