Modular Shimura varieties and forgetful maps

Details Modular Shimura varieties and forgetful maps Modular Shimura varieties and forgetful maps

2003-03-13

arxiv.org/abs/math/0303163v2

Trans. American Math. Soc. 356 (2004), 1535-1550

Mathematics

Number Theory

Minor modifications made

Scientific paper

We consider several maps that occur naturally between modular Shimura
varieties, Hilbert-Blumenthal varieties and the moduli spaces of polarized
abelian varieties when forgetting certain endomorphism structures. We prove
that, up to birational equivalences, these forgetful maps coincide with the
natural projection by suitable abelian groups of Atkin-Lehner involutions.

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