\contentsline {section}{\numberline {1}Introduction}{2}
\contentsline {section}{\numberline {2}The plus/minus $p$-adic $L$-functions}{5}
\contentsline {subsection}{\numberline {2.1}Modular forms on quaternion algebras}{5}
\contentsline {subsection}{\numberline {2.2}Rankin $L$-functions}{7}
\contentsline {section}{\numberline {3}Selmer groups}{15}
\contentsline {subsection}{\numberline {3.1}Local conditions at $\ell \not =p$}{17}
\contentsline {subsection}{\numberline {3.2}Local conditions at $p$}{20}
\contentsline {subsection}{\numberline {3.3}Generalised Selmer groups}{25}
\contentsline {subsection}{\numberline {3.4}Freeness results for Selmer groups}{27}
\contentsline {section}{\numberline {4}Construction of the Euler system}{31}
\contentsline {section}{\numberline {5}Proof of the main result}{36}