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Rational equivalence of
cusps
Shouhei Ma |
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Vol. 5 (2020), No. 3, 395–410
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Abstract |
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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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Keywords
modular variety, Baily–Borel compactification, cusp, Chow
group, Manin–Drinfeld theorem, modular unit, higher Chow
cycle
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Mathematical Subject Classification 2010
Primary: 14C15, 14G35, 11F55, 11F46
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Milestones
Received: 8 August 2019
Accepted: 21 May 2020
Published: 28 July 2020
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Authors |
| Shouhei Ma | |
| Department of Mathematics Tokyo Institute of Technology Tokyo Japan |
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