Rational equivalence of cusps. (English) Zbl 1440.14026

Ma, Shouhei

Ann. \(K\)-Theory 5, No. 3, 395-410 (2020).

Summary: We prove that two cusps of the same dimension in the Baily-Borel compactification of some classical series of modular varieties are linearly dependent in the rational Chow group of the compactification. This gives a higher dimensional analogue of the Manin-Drinfeld theorem. As a consequence, we obtain a higher dimensional generalization of modular units as higher Chow cycles on the modular variety.

MSC:

14C15	(Equivariant) Chow groups and rings; motives
14G35	Modular and Shimura varieties
11F55	Other groups and their modular and automorphic forms (several variables)
11F46	Siegel modular groups; Siegel and Hilbert-Siegel modular and automorphic forms

Keywords:

modular variety; Baily-Borel compactification; cusp; Chow group; Manin-Drinfeld theorem; modular unit; higher Chow cycle

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