Modular Shimura varieties and forgetful maps

Victor Rotger

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Modular Shimura varieties and forgetful maps

Victor Rotger

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Abstract

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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Victor Rotger. 2008-04-25. Modular Shimura varieties and forgetful maps. https://arxiv.org/abs/math/0303163

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