Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On a conjecture of Sharifi and Mazur's Eisenstein ideal   Let $N$ and $p$ be prime numbers $\geq 5$ such that $p$ divides $N-1$. Let
$I$ be Mazur's Eisenstein ideal of level $N$ and $H_+$ be the plus part of
$H_1(X_0(N), \mathbf{Z}_p)$ for the complex conjugation. We give a conjectural
explicit description of the group $I\cdot H_+/I^2\cdot H_+$ in terms of the
second $K$-group of the cyclotomic field $\mathbf{Q}(\zeta_N)$. We prove that
this conjecture follows from a conjecture of Sharifi about some Eisenstein
ideal of level $\Gamma_1(N)$. Following the work of Fukaya--Kato, we prove
partial results on Sharifi's conjecture. This allows us to prove partial
results on our conjecture.

1
The categories of this paper are: cs
6
The categories of this paper are: astro-ph
30
The categories of this paper are: q-alg
32
The categories of this paper are: atom-ph
0
The categories of this paper are: hep-ph
37
The categories of this paper are: supr-con
29
The categories of this paper are: funct-an
13
The categories of this paper are: quant-ph
15
The categories of this paper are: nucl-ex
25
The categories of this paper are: patt-sol
28
The categories of this paper are: alg-geom
16
The categories of this paper are: stat
35
The categories of this paper are: mtrl-th
23
The categories of this paper are: solv-int
7
The categories of this paper are: hep-th
24
The categories of this paper are: dg-ga