Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Rank growth of elliptic curves over $N$-th root extensions   Fix an elliptic curve $E$ over a number field $F$ and an integer $n$ which is
a power of $3$. We study the growth of the Mordell--Weil rank of $E$ after base
change to the fields $K_d = F(\sqrt[2n]{d})$. If $E$ admits a $3$-isogeny, we
show that the average "new rank" of $E$ over $K_d$, appropriately defined, is
bounded as the height of $d$ goes to infinity. When $n = 3$, we moreover show
that for many elliptic curves $E/\mathbb{Q}$, there are no new points on $E$
over $\mathbb{Q}(\sqrt[6]d)$, for a positive proportion of integers $d$. This
is a horizontal analogue of a well-known result of Cornut and Vatsal. The proof
combines our recent work on ranks of abelian varieties in cyclotomic twist
families with a technique we call the "correlation trick", which applies in a
more general context where one is trying to show simultaneous vanishing of
multiple Selmer groups. We also apply this technique to families of twists of
Prym surfaces. As a corollary, we give bounds on the number of rational points
in sextic twist families of bielliptic genus 3 curves.

8
The categories of this paper are: hep-ex
35
The categories of this paper are: mtrl-th
5
The categories of this paper are: gr-qc
9
The categories of this paper are: nlin
13
The categories of this paper are: quant-ph
0
The categories of this paper are: hep-ph
26
The categories of this paper are: bayes-an
11
The categories of this paper are: hep-lat
7
The categories of this paper are: hep-th
18
The categories of this paper are: econ
37
The categories of this paper are: supr-con
10
The categories of this paper are: q-bio
19
The categories of this paper are: eess
6
The categories of this paper are: astro-ph
31
The categories of this paper are: ao-sci
22
The categories of this paper are: chao-dyn