Geodesic
Asymptotic growth of Mordell–Weil ranks of elliptic curves in noncommutative towers
Canadian mathematical bulletin, Tome 65 (2022) no. 4, pp. 1050-1062

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DOI

Let E be an elliptic curve defined over a number field F with good ordinary reduction at all primes above p, and let $F_\infty $ be a finitely ramified uniform pro-p extension of F containing the cyclotomic $\mathbb {Z}_p$-extension $F_{\operatorname {cyc}}$. Set $F^{(n)}$ be the nth layer of the tower, and $F^{(n)}_{\operatorname {cyc}}$ the cyclotomic $\mathbb {Z}_p$-extension of $F^{(n)}$. We study the growth of the rank of $E(F^{(n)})$ by analyzing the growth of the $\lambda $-invariant of the Selmer group over $F^{(n)}_{ \operatorname {cyc}}$ as $n\rightarrow \infty $. This method has its origins in work of A. Cuoco, who studied $\mathbb {Z}_p^2$-extensions. Refined estimates for growth are proved that are close to conjectured estimates. The results are illustrated in special cases.
DOI : 10.4153/S0008439522000108
Mots-clés : Elliptic curves, Iwasawa invariants, Kida’s formula, towers of number fields, asymptotic growth of ranks 
Ray, Anwesh. Asymptotic growth of Mordell–Weil ranks of elliptic curves in noncommutative towers. Canadian mathematical bulletin, Tome 65 (2022) no. 4, pp. 1050-1062. doi: 10.4153/S0008439522000108
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     title = {Asymptotic growth of {Mordell{\textendash}Weil} ranks of elliptic curves in noncommutative towers},
     journal = {Canadian mathematical bulletin},
     pages = {1050--1062},
     year = {2022},
     volume = {65},
     number = {4},
     doi = {10.4153/S0008439522000108},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/S0008439522000108/}
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