Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Semisimple pointed isogeny graphs for abelian varieties   In this paper we show that if $\phi_{i}:A_{i}\rightarrow{A}$ is a semisimple
pointed $K$-rational $\ell$-isogeny graph of order $n$ for a prime $\ell$, then
the group of $\ell$-torsion points $A[\ell](\overline{K})$ contains a subspace
of dimension $n$ generated by $K$-rational points. We also show that the same
result is true for elliptic curves without the semisimplicity condition.
Furthermore, we give an explicit counterexample for abelian varieties of higher
dimension to show that the semisimplicity condition is indeed necessary.

37
The categories of this paper are: supr-con
9
The categories of this paper are: nlin
1
The categories of this paper are: cs
4
The categories of this paper are: cond-mat
32
The categories of this paper are: atom-ph
33
The categories of this paper are: plasm-ph
7
The categories of this paper are: hep-th
10
The categories of this paper are: q-bio
23
The categories of this paper are: solv-int
24
The categories of this paper are: dg-ga
8
The categories of this paper are: hep-ex
29
The categories of this paper are: funct-an
0
The categories of this paper are: hep-ph
19
The categories of this paper are: eess
13
The categories of this paper are: quant-ph
20
The categories of this paper are: acc-phys