Holmstrom Parabolic cohomology

Parabolic cohomology

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Parabolic cohomology

RT (Groups and representation theory), AAG (Arithmetic algebraic geometry)?

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Parabolic cohomology

MR1369426 (97d:11089) Scholl, A. J.(4-DRHM-SL) Vanishing cycles and non-classical parabolic cohomology. Invent. Math. 124 (1996), no. 1-3, 503–524. (interesting)

Notes from André: Motives attached to modular forms. Deligne attached $\ell$-adic parabolic cohomology spaces to modular forms of weight at least two, for some congruence subgroup, using Kuga-Sato varieties. Scholl proved that these cohomology spaces come from a Chow motive. If one wants a decomposition respecting the Hecke action, it seems like one has to pass to motives wrt homological equivalence. I think the following is true: Given a normalised newform of weight at least 2, level $N$, and character $\chi$, with coeffs in a number field $F$, then Scholl constructs a motive in $M_{hom}(\mathbb{Q})_F$ with the right L-factor at good primes.

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Parabolic cohomology

http://mathoverflow.net/questions/76371/parabolic-eisenstein-decomposition-of-cohomology-of-modular-curve

nLab page on Parabolic cohomology