In arithmetic geometry, the **Weil–Châtelet group** or **WC-group** of an algebraic group such as an abelian variety *A* defined over a field *K* is the abelian group of principal homogeneous spaces for *A*, defined over *K*. Tate (1958) named it for François Châtelet (1946) who introduced it for elliptic curves, and Weil (1955), who introduced it for more general groups. It plays a basic role in the arithmetic of abelian varieties, in particular for elliptic curves, because of its connection with infinite descent.

It can be defined directly from Galois cohomology, as *H*^{1}(*G*_{K},*A*), where *G*_{K} is the absolute Galois group of *K*. It is of particular interest for local fields and global fields, such as algebraic number fields. For *K* a finite field, Schmidt (1931) proved that the Weil–Châtelet group is trivial for elliptic curves, and Lang (1956) proved that it is trivial for any algebraic group.