\contentsline {section}{\tocsection {}{}{Introduction}}{1}{section*.2}
\contentsline {section}{\tocsection {}{1}{Cycles and the Griffiths group}}{5}{section.1}
\contentsline {section}{\tocsection {}{2}{Coniveau and the refined Bloch-Beilinson conjecture}}{7}{section.2}
\contentsline {subsection}{\tocsubsection {}{2.1}{The refined conjecture}}{7}{subsection.2.1}
\contentsline {subsection}{\tocsubsection {}{2.2}{Abel-Jacobi}}{8}{subsection.2.2}
\contentsline {subsection}{\tocsubsection {}{2.3}{The Bloch-Kato exponential and logarithm}}{8}{subsection.2.3}
\contentsline {subsection}{\tocsubsection {}{2.4}{Coniveau and the Hodge filtration}}{9}{subsection.2.4}
\contentsline {section}{\tocsection {}{3}{$p$-adic $L$-functions}}{12}{section.3}
\contentsline {subsection}{\tocsubsection {}{3.1}{The Katz $p$-adic $L$-function}}{12}{subsection.3.1}
\contentsline {subsection}{\tocsubsection {}{3.2}{$p$-adic Rankin $L$-series}}{12}{subsection.3.2}
\contentsline {subsection}{\tocsubsection {}{3.3}{Factorization of the $p$-adic Rankin $L$-series}}{13}{subsection.3.3}
\contentsline {section}{\tocsection {}{4}{Generalized Heegner cycles and coniveau}}{14}{section.4}
\contentsline {subsection}{\tocsubsection {}{4.1}{Generalized Heegner cycles}}{14}{subsection.4.1}
\contentsline {subsection}{\tocsubsection {}{4.2}{Fields of definition}}{17}{subsection.4.2}
\contentsline {subsection}{\tocsubsection {}{4.3}{Cycles associated with Grossencharacters}}{18}{subsection.4.3}
\contentsline {section}{\tocsection {}{5}{Miscellany}}{21}{section.5}
\contentsline {subsection}{\tocsubsection {}{5.1}{A non-CM example}}{21}{subsection.5.1}
\contentsline {subsection}{\tocsubsection {}{5.2}{The Fermat quartic revisited}}{24}{subsection.5.2}
\contentsline {section}{\tocsection {Appendix}{A}{Tables}}{28}{section.A}
\contentsline {section}{\tocsection {Appendix}{B}{Integrality of modular forms via intersection theory \\ by Brian Conrad }}{30}{section.B}
\contentsline {subsection}{\tocsubsection {}{B.1}{Introduction}}{30}{subsection.B.1}
\contentsline {subsubsection}{\tocsubsubsection {}{B.1.1}{Integrality and $q$-expansions}}{30}{subsubsection.B.1.1}
\contentsline {subsubsection}{\tocsubsubsection {}{B.1.2}{Moduli stacks}}{30}{subsubsection.B.1.2}
\contentsline {subsubsection}{\tocsubsubsection {}{B.1.3}{Results}}{31}{subsubsection.B.1.3}
\contentsline {subsection}{\tocsubsection {}{B.2}{Intersection-theoretic bounds}}{32}{subsection.B.2}
\contentsline {subsubsection}{\tocsubsubsection {}{B.2.1}{Elimination of $q$-expansions}}{32}{subsubsection.B.2.1}
\contentsline {subsubsection}{\tocsubsubsection {}{B.2.2}{Divisor and intersection theory formalism}}{33}{subsubsection.B.2.2}
\contentsline {subsubsection}{\tocsubsubsection {}{B.2.3}{Geometric calculations}}{39}{subsubsection.B.2.3}
\contentsline {subsection}{\tocsubsection {}{B.3}{Explicit formulas}}{41}{subsection.B.3}
\contentsline {subsubsection}{\tocsubsubsection {}{B.3.1}{Numerology for $X_0(N)$}}{41}{subsubsection.B.3.1}
\contentsline {subsubsection}{\tocsubsubsection {}{B.3.2}{Multiplicity bounds for $\Gamma _0(N)$}}{43}{subsubsection.B.3.2}
\contentsline {section}{\tocsection {Appendix}{}{References}}{46}{section*.3}