Algebra & Number Theory

Moduli of elliptic curves via twisted stable maps

Andrew Niles

Full-text: Open access

Abstract

Abramovich, Corti and Vistoli have studied modular compactifications of stacks of curves equipped with abelian level structures arising as substacks of the stack of twisted stable maps into the classifying stack of a finite group, provided the order of the group is invertible on the base scheme. Recently Abramovich, Olsson and Vistoli extended the notion of twisted stable maps to allow arbitrary base schemes, where the target is a tame stack, not necessarily Deligne–Mumford. We use this to extend the results of Abramovich, Corti and Vistoli to the case of elliptic curves with level structures over arbitrary base schemes; we prove that we recover the compactified Katz–Mazur regular models, with a natural moduli interpretation in terms of level structures on Picard schemes of twisted curves. Additionally, we study the interactions of the different such moduli stacks contained in a stack of twisted stable maps in characteristics dividing the level.

Article information

Source
Algebra Number Theory, Volume 7, Number 9 (2013), 2141-2202.

Dates
Received: 1 August 2012
Revised: 4 January 2013
Accepted: 9 February 2013
First available in Project Euclid: 20 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.ant/1513730090

Digital Object Identifier
doi:10.2140/ant.2013.7.2141

Mathematical Reviews number (MathSciNet)
MR3152011

Zentralblatt MATH identifier
1333.11057

Subjects
Primary: 11G18: Arithmetic aspects of modular and Shimura varieties [See also 14G35]
Secondary: 14K10: Algebraic moduli, classification [See also 11G15] 14H10: Families, moduli (algebraic) 14D23: Stacks and moduli problems 14H52: Elliptic curves [See also 11G05, 11G07, 14Kxx]

Keywords
generalized elliptic curve twisted curve Drinfeld structure moduli stack

Citation

Niles, Andrew. Moduli of elliptic curves via twisted stable maps. Algebra Number Theory 7 (2013), no. 9, 2141--2202. doi:10.2140/ant.2013.7.2141. https://projecteuclid.org/euclid.ant/1513730090


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