The fundamental domain of the tree of \(GL(2)\) over the function field of an elliptic curve
type: Item
instance of: scholarly article
title: The fundamental domain of the tree of \(GL(2)\) over the function field of an elliptic curve
zbMATH Open document ID: 0841.14022
DOI: 10.1215/S0012-7094-93-07204-3
author: S. Takahashi
published in: Duke Mathematical Journal
publication date: 1996-07-16T00:00:00Z
review text: Let \(E\) be an elliptic curve over a field \(k\), and \(k[E]\) be its affine coordinate ring. If \(t\) is a local uniformizer at \(\infty\), then one can embed \(k[E]\) in \(k((t))\). Let \(\Gamma = GL(2,k[E])\), \(K = GL(2,k T)\), \(G = GL(2,k ((t)))\) and \(Z\) be the center of \(G\). Then, following \textit{J.-P. Serre} [``Trees'' (Berlin 1980; Zbl 0548.20018)], one can define a tree structure \(T\) on \(G/KZ\), and the quotient graph \(\Gamma \backslash T\) is well defined. The aim of this paper is to determine the shape of \(\Gamma \backslash T\). More specifically, the author defines a subtree \(S\) of \(T\), such that \(S \approx \Gamma \backslash T\).
Mathematics Subject Classification ID: 14H05
Mathematics Subject Classification ID: 14H52
Mathematics Subject Classification ID: 20E08
zbMATH DE Number: 558995
zbMATH Keywords: tree
zbMATH Keywords: function field of an elliptic curve
reviewed by: Marc Perret
MaRDI profile type: Publication
cites work: On the existence of cusp forms over function fields.
cites work: Automorphe Formen über \({\mathbb{F}}_ q(T)\) mit kleinem Führer. (Automorphic forms over \({\mathbb{F}}_ q(T)\) with small conductor)
cites work: Q3341041
description: scientific article; zbMATH DE number 558995