\contentsline {section}{\tocsection {}{1}{Introduction}}{1}
\contentsline {section}{\tocsection {}{2}{Motives and Chow-Heegner points}}{6}
\contentsline {subsection}{\tocsubsection {}{2.1}{Motives for rational and homological equivalence}}{7}
\contentsline {subsection}{\tocsubsection {}{2.2}{The motive of a Hecke character}}{8}
\contentsline {subsection}{\tocsubsection {}{2.3}{Deligne-Scholl motives}}{9}
\contentsline {subsection}{\tocsubsection {}{2.4}{Modular parametrisations attached to CM forms}}{10}
\contentsline {subsection}{\tocsubsection {}{2.5}{Generalised Heegner cycles and Chow-Heegner points}}{14}
\contentsline {subsection}{\tocsubsection {}{2.6}{A special case}}{16}
\contentsline {section}{\tocsection {}{3}{Chow-Heegner points over $\@mathbb {C}_p$}}{16}
\contentsline {subsection}{\tocsubsection {}{3.1}{The $p$-adic Abel-Jacobi map}}{16}
\contentsline {subsection}{\tocsubsection {}{3.2}{Rationality of Chow-Heegner points over $\@mathbb {C}_p$}}{18}
\contentsline {section}{\tocsection {}{4}{Chow-Heegner points over $\@mathbb {C}$}}{21}
\contentsline {subsection}{\tocsubsection {}{4.1}{The complex Abel-Jacobi map}}{21}
\contentsline {subsection}{\tocsubsection {}{4.2}{Numerical experiments}}{23}
\contentsline {subsubsection}{\tocsubsubsection {}{4.2.1}{Chow-Heegner points of level $1$}}{23}
\contentsline {subsubsection}{\tocsubsubsection {}{4.2.2}{Chow-Heegner points of prime level}}{25}
\contentsline {section}{\tocsection {}{}{References}}{26}