Abelian Surfaces with Anti-holomorphic Multiplication
نویسندگان
چکیده
Let h2 = Sp(4,R)/U(2) be the Siegel upperhalf space of rank 2. The quotient Sp(4,Z)\h2 has three remarkable properties: (a) it is the moduli space of principally polarized abelian surfaces, (b) it has the structure of a quasi-projective complex algebraic variety which is defined over the rational numbers Q, and (c) it has a natural compactification (the BailyBorel Satake compactification) which is defined over the rational numbers. Fix a square-free integer d < 0. One might ask whether similar statements hold for the arithmetic quotient W = SL(2,Od)\H3 (1.0.1)
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