The algebraic functional equation of an elliptic curve at supersingular primes

Since the analytic functional equation holds for the $\pm$-$p$-adic $L$-functions constructed in \cite{pol}, the algebraic functional equation for the $\pm$-Selmer groups is expected to hold as well. In this paper, we show it following the ideas of \cite{gre1} and \cite{kim}.

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Published 1 January 2008