Journal of the Ramanujan Mathematical Society

Volume 32, Issue 1, March 2017 pp. 51–74.

Tame ramification and group cohomology

Authors: Chandan Singh Dalawat and Jung-Jo Lee
Author institution:Harish-Chandra Research Institute, Chhatnag Road, Jhunsi, Allahabad 211 019, India

Summary: We give an intrinsic parametrisation of the set of tamely ramified extensions of a local field with finite residue field and bring to the fore the role played by group cohomology. We show that two natural definitions of the cohomology class of a tamely ramified finite galoisian extension coincide, and can be recovered from the parameter. We also give an elementary proof of Serre's mass formula in the tame case and in the simplest wild case, and we classify tame galoisian extensions of degree the cube of a prime.

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