Symplectic group lattices as Mordell-Weil sublattices
type: Item
instance of: scholarly article
title: Symplectic group lattices as Mordell-Weil sublattices
zbMATH Open document ID: 0869.11057
author: Neil Dummigan
published in: Journal of Number Theory
publication date: 1997-08-17T00:00:00Z
review text: The author deals with a problem raised by \textit{B. H. Gross} [J. Am. Math. Soc. 3, 929-960 (1990; Zbl 0745.11035)]. Gross had produced several interesting families of integral lattices in Euclidean spaces, including certain symplectic group lattice some of which had previously been considered by \textit{R. Gow} [J. Algebra 122, 510-519 (1989; Zbl 0679.20039)]. In the present paper it is shown that these lattices may be realized as sublattices of certain Mordell-Weil lattices that are associated with hyperelliptic curves in odd characteristic \(p\). This result was inspired by a similar one of \textit{N. Elkies} on the Barnes-Wall lattices [ Int. Math. Res. Not. 1994, 343-361 (1994; Zbl 0813.52017)], and is obtained by a cohomological description of the Mordell-Weil lattices over the \(p\)-adic numbers. As a consequence a lower bound on the minimal nonzero norm, due to Elkies, applies to the symplectic group lattices.
Mathematics Subject Classification ID: 11H56
Mathematics Subject Classification ID: 11G05
zbMATH DE Number: 980275
zbMATH Keywords: Mordell-Weil lattice
zbMATH Keywords: symplectic group
zbMATH Keywords: Weil representation
reviewed by: Heinz-Georg Quebbemann
MaRDI profile type: Publication
full work available at URL: jnth.1996.0154
OpenAlex ID: W2043483225
DOI: 10.1006/JNTH.1996.0154
description: scientific article; zbMATH DE number 980275