Arithmetic intersection on a Hilbert modular surface and the Faltings height
نویسندگان
چکیده
منابع مشابه
Arithmetic Intersection on a Hilbert Modular Surface and the Faltings Height
In this paper, we prove an explicit arithmetic intersection formula between arithmetic Hirzebruch-Zagier divisors and arithmetic CM cycles in a Hilbert modular surface over Z. As applications, we obtain the first ‘non-abelian’ Chowla-Selberg formula, which is a special case of Colmez’s conjecture; an explicit arithmetic intersection formula between arithmetic Humbert surfaces and CM cycles in t...
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is finite under the following equivalence (cf. Theorem 3.1). For stable curves X and Y over OK , X is equivalent to Y if X ⊗OK OK′ ≃ Y ⊗OK OK′ for some finite extension field K ′ of K. In §1, we will consider semistability of the kernel of H(C,L) ⊗ OC → L, which gives a generalization of [PR]. In §2, an inequality of self-intersection and height will be treated. Finally, §3 is devoted to finite...
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We prove an arithmetic version of a theorem of Hirzebruch and Zagier saying that Hirzebruch-Zagier divisors on a Hilbert modular surface are the coefficients of an elliptic modular form of weight two. Moreover, we determine the arithmetic selfintersection number of the line bundle of modular forms equipped with its Petersson metric on a regular model of a Hilbert modular surface, and study Falt...
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In this paper, we obtain an explicit arithmetic intersection formula on a Hilbert modular surface between the diagonal embedding of the modular curve and a CM cycle associated to a nonbiquadratic CM quartic field. This confirms a special case of the author’s conjecture with J. Bruinier, and is a generalization of the beautiful factorization formula of Gross and Zagier on singular moduli. As an ...
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In this paper, we reinterpret the Colmez conjecture on the Faltings height of CM abelian varieties in terms of Hilbert (and Siegel) modular forms. We construct an elliptic modular form involving the Faltings height of a CM abelian surface and arithmetic intersection numbers, and prove that the Colmez conjecture for CM abelian surfaces is equivalent to the cuspidality of this modular form.
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ژورنال
عنوان ژورنال: Asian Journal of Mathematics
سال: 2013
ISSN: 1093-6106,1945-0036
DOI: 10.4310/ajm.2013.v17.n2.a4