In his Corvallis article, Langlands [L, Sec. 6] stated a conjecture that identifies the conjugate of a Shimura variety by an automorphism of C with the Shimura variety defined by different data, and he sketched a proof that his conjecture im- plies the existence of canonical models. However, as J. Wildeshaus and others have pointed out to me, it is not obvious that the descent maps defined by Lang- lands satisfy the continuity condition necessary for the descent to be effective. In this note, I prove that they do satisfy this condition and hence that Langlands's conjecture does imply the existence of canonical modelswthis is our only proof of the existence of these models for a general Shimura variety. The proof is quite short and elementary. I give it in Section 2 after reviewing some generalities on the descent of varieties in Section l.
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