Vol. 5, No. 3, 2020

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Rational equivalence of cusps

Shouhei Ma

Vol. 5 (2020), No. 3, 395–410
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.

Keywords
modular variety, Baily–Borel compactification, cusp, Chow group, Manin–Drinfeld theorem, modular unit, higher Chow cycle
Mathematical Subject Classification 2010
Primary: 14C15, 14G35, 11F55, 11F46
Milestones
Received: 8 August 2019
Accepted: 21 May 2020
Published: 28 July 2020
Authors
Shouhei Ma
Department of Mathematics
Tokyo Institute of Technology
Tokyo
Japan