Triangulordinary Selmer Groups
Jonathan Pottharst

TL;DR
This paper introduces triangulordinary Galois representations over p-adic fields, describing their local conditions and proposing a variational approach to define associated Selmer groups along the Coleman--Mazur eigencurve.
Contribution
It defines triangulordinary representations, characterizes their local conditions, and proposes a new variational framework for Selmer groups on the eigencurve.
Findings
Description of Bloch--Kato local conditions for triangulordinary representations
Introduction of a variational approach to Selmer groups
Potential extension of Selmer group definitions to nonordinary loci
Abstract
Let be a prime number, and let be a -adic local field. We study a class of semistable -adic Galois representations of , which we call {\it triangulordinary} because it includes the ordinary ones yet allows non-\'etale behavior in the associated -modules over the Robba ring. Our main result provides a description of the Bloch--Kato local condition of such representations. We also propose a program, using variational techniques, that would give a definition of the Selmer group along the eigencurve of Coleman--Mazur, including notably its nonordinary locus.
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Taxonomy
TopicsAdvanced Algebra and Geometry · Geometric and Algebraic Topology · Geometry and complex manifolds
