Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A geometric perspective on the Breuil-M\'ezard conjecture   Let p > 2 be prime. We state and prove (under mild hypotheses on the residual
representation) a geometric refinement of the Breuil-M\'ezard conjecture for
2-dimensional mod p representations of the absolute Galois group of Qp. We also
state a conjectural generalisation to n-dimensional representations of the
absolute Galois group of an arbitrary finite extension of Qp, and give a
conditional proof of this conjecture, subject to a certain R = T-type theorem
together with a strong version of the weight part of Serre's conjecture for
rank n unitary groups. We deduce an unconditional result in the case of
two-dimensional potentially Barsotti-Tate representations.

17
The categories of this paper are: q-fin
7
The categories of this paper are: hep-th
20
The categories of this paper are: acc-phys
0
The categories of this paper are: hep-ph
23
The categories of this paper are: solv-int
1
The categories of this paper are: cs
21
The categories of this paper are: adap-org
29
The categories of this paper are: funct-an
15
The categories of this paper are: nucl-ex
14
The categories of this paper are: math-ph
34
The categories of this paper are: chem-ph
18
The categories of this paper are: econ
30
The categories of this paper are: q-alg
37
The categories of this paper are: supr-con
24
The categories of this paper are: dg-ga
28
The categories of this paper are: alg-geom