Group cohomology of the universal ordinary distribution

Yi Ouyang; Greg W. Anderson

doi:10.1515/crll.2001.057

Group cohomology of the universal ordinary distribution

Yi Ouyang, Greg W. Anderson

School of Mathematics

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Abstract

For any odd squarefree integer r, we obtain a complete description of the G_r = Gal(ℚ(μ_r)/ℚ) group cohomology of the universal ordinary distribution U_r in this paper. Moreover, for M a fixed integer dividing ℓ - 1 for all prime factors ℓ of r, we study the cohomology group H*(G_r, U_r/MU_r). In particular, we explain the construction of the elements κ_r′ for r′|r in Rubin [9], which come exactly from a certain ℤ/Mℤ-basis of the cohomology group H⁰(G_r, U_r/MU_r) through an evaluation map.

Original language	English (US)
Pages (from-to)	1-32
Number of pages	32
Journal	Journal fur die Reine und Angewandte Mathematik
Volume	537
DOIs	https://doi.org/10.1515/crll.2001.057
State	Published - 2001

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Group cohomology of the universal ordinary distribution

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