Rank parity for congruent supersingular elliptic curves
Copyright policy )Rank parity for congruent supersingular elliptic curves
A recent paper of Shekhar compares the ranks of elliptic curves E 1 E_1 and E 2 E_2 for which there is an isomorphism E 1 [ p ] ≃ E 2 [ p ] E_1[p] \simeq E_2[p] as G a l ( Q ¯ / Q ) \mathrm {Gal}(\bar {\mathbf {Q}}/\mathbf {Q}) -modules, where p p is a prime of good ordinary reduction for both curves. In this paper we prove an analogous result in the case where p p is a prime of good supersingular reduction.
- King’s University United States
- Union College United States
Iwasawa Theory, Mathematics - Number Theory, Galois representations, parity conjecture, Selmer groups, Elliptic curves over global fields, analytical rank, elliptic curves, FOS: Mathematics, Elliptic curves, supersingular elliptic curves, Number Theory (math.NT), Iwasawa theory
Iwasawa Theory, Mathematics - Number Theory, Galois representations, parity conjecture, Selmer groups, Elliptic curves over global fields, analytical rank, elliptic curves, FOS: Mathematics, Elliptic curves, supersingular elliptic curves, Number Theory (math.NT), Iwasawa theory
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