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- W2023357096 abstract "Let E be a totally real number field of degree d over Q. We give a method for constructing a set of Hilbert modular cuspforms f1, . . . , fd with the following property. Let K be the fraction field of a complete dvr A, and let X/K be a Hilbert-Blumenthal abelian variety with multiplicative reduction and real multiplication by the ring of integers of E. Suppose n is an integer such that n divides the minimal valuation of fi(X) for all i. Then X[n′]/K extends to a finite flat group scheme over A, where n′ is a divisor of n with n′/n bounded by a constant depending only on f1, . . . , fd. When E = Q, the theorem reduces to a well-known property of f1 = ∆. In the cases E = Q( √ 2) and E = Q( √ 5), we produce the desired pairs of Hilbert modular forms explicitly and show how they can be used to compute the group of Neron components of a Hilbert-Blumenthal abelian variety with real multiplication by E." @default.
- W2023357096 created "2016-06-24" @default.
- W2023357096 creator A5071941381 @default.
- W2023357096 date "2001-01-09" @default.
- W2023357096 modified "2023-10-14" @default.
- W2023357096 title "Finite flatness of torsion subschemes of Hilbert-Blumenthal abelian varieties" @default.
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- W2023357096 doi "https://doi.org/10.1515/crll.2001.016" @default.
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