Rational equivalence of cusps
Algebraic Geometry
2020-07-29 v3 Number Theory
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.
Cite
@article{arxiv.1902.08381,
title = {Rational equivalence of cusps},
author = {Shouhei Ma},
journal= {arXiv preprint arXiv:1902.08381},
year = {2020}
}