Abstract
Let F be a real quadratic field of discriminant d F and different \( {\mathfrak D} \) F , and denote by σ ε Gal(F/ℚ) the nontrivial Galois automorphism of F. Associated to F is a Hilbert modular surface M. The algebraic stack M is defined as the moduli space of abelian surfaces A equipped with an action of \( {\mathcal O} \) F , and with an \( {\mathcal O} \) F -linear principal polarization; see Chap. 3 for more details. We refer to such A as \( {\mathcal O} \) F -polarized RM abelian surfaces. The abbreviation RM stands for real multiplication, and the \( {\mathcal O} \) F in \( {\mathcal O} \) F -polarization indicates that the polarization is principal (in much of the text we allow a more general class of polarizations; see Sect. 3.1). It is known that M is regular, flat over Spec(ℤ) of relative dimension two, and smooth over Spec(ℤ[1/d F ]).
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© 2011 Springer-Verlag Berlin Heidelberg
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Howard, B., Yang, T. (2011). Introduction. In: Intersections of Hirzebruch–Zagier Divisors and CM Cycles. Lecture Notes in Mathematics(), vol 2041. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-23979-3_1
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DOI: https://doi.org/10.1007/978-3-642-23979-3_1
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Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-23978-6
Online ISBN: 978-3-642-23979-3
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