Final remarks on local discriminants

Details Final remarks on local discriminants Final remarks on local discriminants

2009-12-15

arxiv.org/abs/0912.2829v3

Journal of the Ramanujan Mathematical Society {\bf 25} (2010) 4, 419--432

Mathematics

Number Theory

14 pages; new section 6 on the contribution of cyclic extensions to Serre's degree-p mass formula

Scientific paper

We show how the ramification filtration on the maximal elementary abelian p-extension (p prime) on a local number field of residual characteristic p can be derived using only Kummer theory and a certain orthogonality relation for the Kummer pairing, even in the absence of a primitive p-th root of 1; the case of other local fields with finite residue fields was treated earlier. In all cases, we compute the contribution of cyclic extensions to Serre's degree-$p$ mass formula.

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