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- W3044988891 abstract "Let $K/F$ be a finite Galois extension of number fields and $sigma$ be an absolutely irreducible, self-dual representation of $mathrm{Gal}(K/F)$. Let $p$ be an odd prime and consider two elliptic curves $E_1, E_2$ with good, ordinary reduction at primes above $p$ and equivalent mod-$p$ Galois representations. In this article, we study the variation of the parity of the multiplicities of $sigma$ in the representation space associated to the $p^infty$-Selmer group of $E_i$ over $K$. We also compare the root numbers for the twist of $E_i/F$ by $sigma$ and show that the $p$-parity conjecture holds for the twist of $E_1/F$ by $sigma$ if and only if it holds for the twist of $E_2/F$ by $sigma$. We also express Mazur-Rubin-Nekovař's arithmetic local constants in terms of certain local Iwasawa invariants." @default.
- W3044988891 created "2020-07-29" @default.
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- W3044988891 date "2020-07-25" @default.
- W3044988891 modified "2023-09-27" @default.
- W3044988891 title "Multiplicities in Selmer groups and root numbers for Artin twists" @default.
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