Intersections over modular curves
type: Item
instance of: scholarly article
title: Intersections over modular curves
zbMATH Open document ID: 0812.14013
DOI: 10.1007/BF03026554
published in: Manuscripta Mathematica
publication date: 1994-02-07T00:00:00Z
full work available at URL: https://eudml.org/doc/155876
review text: Let \(\Gamma \subset S L_ 2 (\mathbb{Z})\) be a subgroup of finite index containing \(-I\), \(Y\) the quotient of the complex upper half plane by \(\Gamma\), \(X\) the associated compact Riemann surface, and \(C = X - Y\). \textit{Manin} gave a description of the relative homology group \(H_ 1 (X,C; \mathbb{Z})\) in terms of modular symbols. Here, the author describes \(H_ 1 (Y; \mathbb{Z})\) as a subquotient of the group of \(\mathbb{Z}\)-valued functions on the coset space \(\Gamma \backslash SL_ 2 (\mathbb{Z})\). He then gives a formula for the intersection of a modular symbol and a suitable function, thus determining the intersection pairing \(H_ 1 (X,C; \mathbb{Z}) \times H_ 1 (Y; \mathbb{Z}) \to \mathbb{Z}\).
Mathematics Subject Classification ID: 14F43
Mathematics Subject Classification ID: 14H25
Mathematics Subject Classification ID: 14G35
Mathematics Subject Classification ID: 11G18
zbMATH DE Number: 492787
zbMATH Keywords: modular curve
zbMATH Keywords: intersection of a modular symbol
zbMATH Keywords: intersection pairing
author: Loïc Merel
MaRDI profile type: Publication
cites work: Generators and relations of \(\Gamma_0\)(N)
cites work: Q5643279
cites work: PARABOLIC POINTS AND ZETA-FUNCTIONS OF MODULAR CURVES
cites work: Q5631207
cites work: Modular symbols of arbitrary weight
description: scientific article; zbMATH DE number 492787