Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: $q$-deformation with ($\varphi, \Gamma$) structure of the de Rham
  cohomology of the Legendre family of elliptic curves   In the late '60s, B. Dwork studied a Frobenius structure compatible with the
classical hypergeometric differential equation with parameters
$\left(\frac{1}{2},\frac{1}{2} ; 1 \right)$ by analyzing behavior of solutions
of the differential equation under Frobenius transformation. Recently, P.
Scholze conjectured the existence of $q$-de Rham cohomology groups for any
$\mathbb{Z}$-scheme. In this paper, we give a Frobenius structure compatible
with the $q$-hypergeometric differential equation with parameters
$(q^{\frac12},q^{\frac12};q)$ by showing a $q$-analogue of some results of
Dwork. This construction gives a $q$-deformation with
$(\varphi,\Gamma)$-structure over $\mathbb{Z}_p[[q-1]][[\lambda]]$ of the de
Rham cohomology of the $p$-adic Legendre family of elliptic curves which has
Frobenius structure and connection.

14
The categories of this paper are: math-ph
8
The categories of this paper are: hep-ex
15
The categories of this paper are: nucl-ex
0
The categories of this paper are: hep-ph
30
The categories of this paper are: q-alg
12
The categories of this paper are: nucl-th
1
The categories of this paper are: cs
36
The categories of this paper are: cmp-lg
25
The categories of this paper are: patt-sol
35
The categories of this paper are: mtrl-th
9
The categories of this paper are: nlin
31
The categories of this paper are: ao-sci
37
The categories of this paper are: supr-con
19
The categories of this paper are: eess
22
The categories of this paper are: chao-dyn
21
The categories of this paper are: adap-org