\contentsline {section}{\tocsection {}{}{Introduction}}{1}{section*.2}%
\contentsline {section}{\tocsection {}{1}{Preliminaries }}{4}{section.1}%
\contentsline {section}{\tocsection {}{2}{Green's functions on CM points in $\cH _p$}}{8}{section.2}%
\contentsline {subsection}{\tocsubsection {}{2.1}{Shimura curves}}{8}{subsection.2.1}%
\contentsline {subsection}{\tocsubsection {}{2.2}{Summary of the construction}}{9}{subsection.2.2}%
\contentsline {subsection}{\tocsubsection {}{2.3}{The homology of divisors}}{9}{subsection.2.3}%
\contentsline {subsection}{\tocsubsection {}{2.4}{The cohomology of locally finite divisors}}{10}{subsection.2.4}%
\contentsline {subsection}{\tocsubsection {}{2.5}{The $p$-adic period pairing}}{10}{subsection.2.5}%
\contentsline {subsection}{\tocsubsection {}{2.6}{Unitary divisors}}{12}{subsection.2.6}%
\contentsline {subsection}{\tocsubsection {}{2.7}{Rigid meromorphic functions and principal divisors}}{12}{subsection.2.7}%
\contentsline {subsection}{\tocsubsection {}{2.8}{$p$-adic N\'eron symbols and Green's functions}}{14}{subsection.2.8}%
\contentsline {section}{\tocsection {}{3}{Green's functions on RM cycles in $\cH \times \cH _p$}}{15}{section.3}%
\contentsline {subsection}{\tocsubsection {}{3.1}{The set-up}}{15}{subsection.3.1}%
\contentsline {subsection}{\tocsubsection {}{3.2}{Cohomological preliminaries}}{16}{subsection.3.2}%
\contentsline {subsection}{\tocsubsection {}{3.3}{RM cycles and divisor-valued homology classes}}{17}{subsection.3.3}%
\contentsline {subsection}{\tocsubsection {}{3.4}{RM cycles and divisor-valued cohomology classes}}{17}{subsection.3.4}%
\contentsline {subsection}{\tocsubsection {}{3.5}{The homology of divisors}}{18}{subsection.3.5}%
\contentsline {subsection}{\tocsubsection {}{3.6}{The cohomology of locally finite divisors}}{19}{subsection.3.6}%
\contentsline {subsection}{\tocsubsection {}{3.7}{The $p$-adic period pairing}}{19}{subsection.3.7}%
\contentsline {subsection}{\tocsubsection {}{3.8}{Unitary classes}}{21}{subsection.3.8}%
\contentsline {subsection}{\tocsubsection {}{3.9}{Rigid meromorphic cocycles and principal classes}}{22}{subsection.3.9}%
\contentsline {subsection}{\tocsubsection {}{3.10}{$p$-adic N\'eron symbols and Green's functions for RM cycles}}{23}{subsection.3.10}%
\contentsline {subsection}{\tocsubsection {}{3.11}{The local trace of $G_p(\alpha _1,\alpha _2)$ }}{25}{subsection.3.11}%
\contentsline {section}{\tocsection {}{}{References}}{27}{section*.4}%