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Compatibility of arithmetic and algebraic local constants (the case
$\ell \neq p$)
Published online by Cambridge University Press: 08 April 2015
Abstract
We show that arithmetic local constants attached by Mazur and Rubin to pairs of self-dual Galois representations which are congruent modulo a prime number $p>2$ are compatible with the usual local constants at all primes not dividing
$p$ and in two special cases also at primes dividing
$p$. We deduce new cases of the
$p$-parity conjecture for Selmer groups of abelian varieties with real multiplication (Theorem 4.14) and elliptic curves (Theorem 5.10).
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- Research Article
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- © The Author 2015
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