Hilbert Modular Varieties of Galois Quartic Fields

doi:10.1006/jnth.1997.2074

Journal of Number Theory

Volume 63, Issue 1, March 1997, Pages 47-58

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Abstract

Letkbe a totally real number field of degreenoverQwith ring of integers $O$ _k. The Hilbert modular variety ofkis a desingularization of the (natural) compactification of PSL₂( $O$ _k)\ $H$ ⁿ. This paper focuses on Hilbert modular varieties of Galois quartic fields containing units of norm −1. The main result is that each of these varieties has arithmetic genus greater than one and hence is not rational.

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^☆: This material is based on work supported by the National Science Foundation under Grant No. DMS-9115349

^☆☆: Communicated by H. Stark

Journal of Number Theory

Regular ArticleHilbert Modular Varieties of Galois Quartic Fields☆,☆☆

Abstract

Regular Article
Hilbert Modular Varieties of Galois Quartic Fields☆,☆☆