Algebra & Number Theory
- Algebra Number Theory
- Volume 7, Number 9 (2013), 2141-2202.
Moduli of elliptic curves via twisted stable maps
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.
Algebra Number Theory, Volume 7, Number 9 (2013), 2141-2202.
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
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
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]
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