Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Stable $\mathbb{I}$-free lattices and the two-variable algebraic
  $p$-adic $L$-functions in residually reducible Hida deformation   This paper is a continuation of the author's previous work, where we studied
the variation of the number of isomorphic classes of $G_{\mathbb{Q}}$-stable
lattices in p-adic families of residually reducible ordinary Galois
representations. In this paper, we study the number of isomorphic classes of
$G_{\mathbb{Q}}$-stable free lattices in a residually reducible Hida
deformation and the variation of their related two-variable algebraic $p$-adic
$L$-functions. This result gives an answer of a question asked by Ochiai.

5
The categories of this paper are: gr-qc
1
The categories of this paper are: cs
13
The categories of this paper are: quant-ph
12
The categories of this paper are: nucl-th
15
The categories of this paper are: nucl-ex
23
The categories of this paper are: solv-int
4
The categories of this paper are: cond-mat
24
The categories of this paper are: dg-ga
11
The categories of this paper are: hep-lat
29
The categories of this paper are: funct-an
3
The categories of this paper are: physics
36
The categories of this paper are: cmp-lg
0
The categories of this paper are: hep-ph
28
The categories of this paper are: alg-geom
33
The categories of this paper are: plasm-ph
7
The categories of this paper are: hep-th