Abstract
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.
Citation
Dan Petersen. "Cusp form motives and admissible $G$-covers." Algebra Number Theory 6 (6) 1199 - 1221, 2012. https://doi.org/10.2140/ant.2012.6.1199
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