Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A quaternionic construction of $p$-adic singular moduli   Rigid meromorphic cocycles were introduced by Darmon and Vonk as a
conjectural $p$-adic extension of the theory of singular moduli to real
quadratic base fields. They are certain cohomology classes of
$\mathrm{SL}_2(\mathbb{Z}[1/p])$ which can be evaluated at real quadratic
irrationalities and the values thus obtained are conjectured to lie in
algebraic extensions of the base field. In this article we present a similar
construction of cohomology casses in which $\mathrm{SL}_2(\mathbb{Z}[1/p])$ is
replaced by an order in an indefinite quaternion algebra over a totally real
number field $F$. These quaternionic cohomology classes can be evaluated at
elements in almost totally complex extensions $K$ of $F$, and we conjecture
that the corresponding values lie in algebraic extensions of $K$. We also
report on extensive numerical evidence for this algebraicity conjecture.

26
The categories of this paper are: bayes-an
17
The categories of this paper are: q-fin
9
The categories of this paper are: nlin
31
The categories of this paper are: ao-sci
33
The categories of this paper are: plasm-ph
1
The categories of this paper are: cs
29
The categories of this paper are: funct-an
27
The categories of this paper are: comp-gas
32
The categories of this paper are: atom-ph
14
The categories of this paper are: math-ph
21
The categories of this paper are: adap-org
19
The categories of this paper are: eess
5
The categories of this paper are: gr-qc
16
The categories of this paper are: stat
15
The categories of this paper are: nucl-ex
8
The categories of this paper are: hep-ex