Cusp form motives and admissible G-covers
2012 (English)In: Algebra & Number Theory, ISSN 1937-0652, Vol. 6, no 6, 1199-1221 p.Article in journal (Refereed) Published
There is a natural S-n-action on the moduli space (M) over bar (1,n) (B(Z/mZ)(2)) of twisted stable maps into the stack B(Z/mZ)(2), and so its cohomology may be decomposed into irreducible S-n-representations. Working over Spec Z [1/m] we show that the alternating part of the cohomology of one of its connected components is exactly the cohomology associated to cusp forms for Gamma(m). 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.
Place, publisher, year, edition, pages
2012. Vol. 6, no 6, 1199-1221 p.
Chow motive, cusp form, admissible cover, twisted curve, level structure
Algebra and Logic
IdentifiersURN: urn:nbn:se:kth:diva-48905DOI: 10.2140/ant.2012.6.1199ISI: 000307648000005ScopusID: 2-s2.0-84865483777OAI: oai:DiVA.org:kth-48905DiVA: diva2:458842
QC 20120924. Updated from submitted to published.2011-11-242011-11-242012-09-24Bibliographically approved