Frobenius modules over multivariate Robba rings

Abstract

We describe a class of multivariate series rings generalizing the usual Robba ring over a p-adic field, and give a basic development of phi-modules over such rings. This makes it possible to give a unified survey of a number of recent developments in p-adic Hodge theory.

41 pages; v3: corrected treatment of locally analytic vectors in section 12

References in corpus (4)

• Slope filtrations revisited
• Slope filtrations for relative Frobenius
• Density of potentially crystalline representations of fixed weight
• New methods for (phi, Gamma)-modules

Cited by in corpus (4)

• Drinfeld's lemma for perfectoid spaces and overconvergence of multivariate $(\phi ,\Gamma )$-modules
• Multivariable $(\phi ,\Gamma )$-modules and smooth $o$-torsion representations
• On differential modules associated to de Rham representations in the imperfect residue field case
• Analytic Geometry and Hodge-Frobenius Structure Continued