Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The third homology of $\mathrm{SL}_2(\mathbb{Q})$   We calculate the third homology of $\mathrm{SL}_2(\mathbb{Q})$ with
half-integral coefficients. Corresponding to each prime $p$ there is an
operator on this group with square the identity. The kernel of the (split
surjective) homomorphism to the indecomposable $K_3$ of $\mathbb{Q}$ is a the
direct sum over all primes of the $(-1)$-eigenspaces of these operators. The
$(-1)$-eigenspace of the operator corresponding to the prime $p$ is cyclic of
order the odd part of $p+1$.

11
The categories of this paper are: hep-lat
30
The categories of this paper are: q-alg
28
The categories of this paper are: alg-geom
4
The categories of this paper are: cond-mat
7
The categories of this paper are: hep-th
34
The categories of this paper are: chem-ph
19
The categories of this paper are: eess
16
The categories of this paper are: stat
3
The categories of this paper are: physics
14
The categories of this paper are: math-ph
31
The categories of this paper are: ao-sci
35
The categories of this paper are: mtrl-th
22
The categories of this paper are: chao-dyn
18
The categories of this paper are: econ
33
The categories of this paper are: plasm-ph
24
The categories of this paper are: dg-ga