Triangulordinary Selmer Groups

Abstract

Let $p$ be a prime number, and let $K$ be a $p$-adic local field. We study a class of semistable $p$-adic Galois representations of $K$, which we call {\it triangulordinary} because it includes the ordinary ones yet allows non-étale behavior in the associated $(\varphi ,{\Gamma }_K)$-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.

39 pages

References in corpus (1)

• Slope filtrations for relative Frobenius

Cited by in corpus (1)

• Ranks of Selmer groups in an analytic family