Periods of Quaternionic Shimura Varieties. I.

Darmon’s points and quaternionic Shimura varieties

In this paper, we generalize a conjecture due to Darmon and Logan (see [DL03] and [Dar04], chapter 8) in an adelic setting. We study the relation between our construction and Kudla’s works on cycles on orthogonal Shimura varieties. This relation allows us to conjecture a Gross-Kohnen-Zagier theorem for Darmon’s points.

Cohomology of quaternionic Shimura varieties at parahoric levels

On the Zeta Function of Quaternionic Shimura Varieties

Shimura Varieties and Moduli

Connected Shimura varieties are the quotients of hermitian symmetric domains by discrete groups defined by congruence conditions. We examine their relation with moduli varieties.

Descent for Shimura Varieties

Wildeshaus and others have pointed out to me that it is not obvious that the descent maps on a Shimura variety given by Langlands’s Conjugacy Conjecture (Langlands 1979, Section 6) satisfy the continuity condition required for the descent to be effective. The following provides one proof of this (maybe not the best). Since the family (fσ) satisfying the conditions (a,b,c) below is unique (by th...