Properties of Extended Robba Rings
Peter Wear
TL;DR
This paper explores the properties of extended Robba rings in p-adic Hodge theory, establishing their regularity and excellence, which are crucial for constructing the Fargues-Fontaine curve.
Contribution
It proves fundamental properties of extended Robba rings, such as regularity and excellence, extending known results from rigid analytic geometry.
Findings
Extended Robba rings are regular.
They are shown to be excellent rings.
Results support their use in constructing the Fargues-Fontaine curve.
Abstract
We extend the analogy between the extended Robba rings of p-adic Hodge theory and the one-dimensional affinoid algebras of rigid analytic geometry, proving some fundamental properties that are well known in the latter case. In particular, we show that these rings are regular and excellent. The extended Robba rings are of interest as they are used to build the Fargues-Fontaine curve.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Commutative Algebra and Its Applications · Homotopy and Cohomology in Algebraic Topology