Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On categories of (phi, Gamma)-modules   Let K be a complete discretely valued field of mixed characteristics (0, p)
with perfect residue field. One of the central objects of study in p-adic Hodge
theory is the category of continuous representations of the absolute Galois
group of K on finite-dimensional Qp-vector spaces. In recent years, it has
become clear that this category can be studied more effectively by embedding it
into the larger category of (phi, Gamma)-modules; this larger category plays a
role analogous to that played by the category of vector bundles on a compact
Riemann surface in the Narasimhan-Seshadri theorem on unitary representations
of the fundamental group of said surface. This category turns out to have a
number of distinct natural descriptions, which on one hand suggests the
naturality of the construction, but on the other hand forces one to use
different descriptions for different applications. We provide several of these
descriptions and indicate how to translate certain key constructions, which
were originally given in the context of modules over power series rings, to the
more modern context of perfectoid algebras and spaces.

32
The categories of this paper are: atom-ph
29
The categories of this paper are: funct-an
3
The categories of this paper are: physics
23
The categories of this paper are: solv-int
12
The categories of this paper are: nucl-th
1
The categories of this paper are: cs
8
The categories of this paper are: hep-ex
19
The categories of this paper are: eess
30
The categories of this paper are: q-alg
0
The categories of this paper are: hep-ph
13
The categories of this paper are: quant-ph
37
The categories of this paper are: supr-con
18
The categories of this paper are: econ
15
The categories of this paper are: nucl-ex
24
The categories of this paper are: dg-ga
22
The categories of this paper are: chao-dyn