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