Normalized Indexing for Ramification Subgroups

2025/09/18 by Stephen DeBacker, David Schwein, DeBacker, Stephen +3
Mathematics · #Advanced Algebra and Geometry #Homotopy and Cohomology in Algebraic Topology #Algebraic Geometry and Number Theory

paper · pdf · doi:10.48550/arxiv.2509.14881

Abstract

This expository note introduces a normalization of the indexing of the lower and upper numbering ramification subgroups of local class field theory. We then look at how this normalization interacts with base change for Langlands parameters.

Citations

• Depth Preservation and Close-Field Transfer in the Local Langlands Correspondence
• Comparison of the depths on both sides of the local Langlands\n correspondence for Weil-restricted groups (with appendix by Jessica Fintzen)

Related

• On Abhyankar's lemma about ramification indices
• Invitation to higher local fields, Part I, section 17: An approach to higher ramification theory
• Field patching, factorization and local-global principles
• The Norm Index Theorem (An Analytic Proof)
• On the numerology of ramification data for power series in\n characteristic p