Periods of Quaternionic Shimura Varieties. I.
نویسندگان
چکیده
We study quadratic periods on quaternionic Shimura varieties and formulate an integral refinement of Shimura's conjecture regarding Petersson inner products automorphic forms that are related by the Jacquet-Langlands correspondence. The main result is this implied another (Conjecture D below) integrality theta lifts between certain unitary groups.
منابع مشابه
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.
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Connected Shimura varieties are the quotients of hermitian symmetric domains by discrete groups defined by congruence conditions. We examine their relation with moduli varieties.
متن کاملDescent 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...
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ژورنال
عنوان ژورنال: Contemporary mathematics
سال: 2021
ISSN: ['2705-1056', '2705-1064']
DOI: https://doi.org/10.1090/conm/762/15363