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2013 Moduli of elliptic curves via twisted stable maps
Andrew Niles
Algebra Number Theory 7(9): 2141-2202 (2013). DOI: 10.2140/ant.2013.7.2141


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.


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Andrew Niles. "Moduli of elliptic curves via twisted stable maps." Algebra Number Theory 7 (9) 2141 - 2202, 2013.


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

zbMATH: 1333.11057
MathSciNet: MR3152011
Digital Object Identifier: 10.2140/ant.2013.7.2141

Primary: 11G18
Secondary: 14D23 , 14H10 , 14H52 , 14K10

Keywords: Drinfeld structure , generalized elliptic curve , moduli stack , twisted curve

Rights: Copyright © 2013 Mathematical Sciences Publishers


Vol.7 • No. 9 • 2013
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