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2020 Rational equivalence of cusps
Shouhei Ma
Ann. K-Theory 5(3): 395-410 (2020). DOI: 10.2140/akt.2020.5.395

Abstract

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.

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Shouhei Ma. "Rational equivalence of cusps." Ann. K-Theory 5 (3) 395 - 410, 2020. https://doi.org/10.2140/akt.2020.5.395

Information

Received: 8 August 2019; Accepted: 21 May 2020; Published: 2020
First available in Project Euclid: 11 August 2020

zbMATH: 07237237
MathSciNet: MR4132742
Digital Object Identifier: 10.2140/akt.2020.5.395

Subjects:
Primary: 11F46 , 11F55 , 14C15 , 14G35

Keywords: Baily–Borel compactification , Chow group , cusp , higher Chow cycle , Manin–Drinfeld theorem , modular unit , modular variety

Rights: Copyright © 2020 Mathematical Sciences Publishers

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Vol.5 • No. 3 • 2020
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