Algebra & Number Theory
- Algebra Number Theory
- Volume 6, Number 6 (2012), 1199-1221.
Cusp form motives and admissible $G$-covers
There is a natural -action on the moduli space of twisted stable maps into the stack , and so its cohomology may be decomposed into irreducible -representations. Working over we show that the alternating part of the cohomology of one of its connected components is exactly the cohomology associated to cusp forms for . In particular this offers an alternative to Scholl’s construction of the Chow motive associated to such cusp forms. This answers in the affirmative a question of Manin on whether one can replace the Kuga–Sato varieties used by Scholl with some moduli space of pointed stable curves.
Algebra Number Theory, Volume 6, Number 6 (2012), 1199-1221.
Received: 18 March 2011
Accepted: 18 October 2011
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: 14H10: Families, moduli (algebraic)
Petersen, Dan. Cusp form motives and admissible $G$-covers. Algebra Number Theory 6 (2012), no. 6, 1199--1221. doi:10.2140/ant.2012.6.1199. https://projecteuclid.org/euclid.ant/1513729865