\relax 
\citation{bdp1}
\citation{beilinson}
\citation{bloch-crelle}
\citation{bloch-duke}
\citation{jannsen-banff}
\citation{bdp1}
\citation{bloch-duke}
\@writefile{toc}{\contentsline {section}{\tocsection {}{}{Introduction}}{2}}
\newlabel{sec:intro}{{}{2}}
\newlabel{thm:intro}{{1}{2}}
\citation{scholl}
\citation{bdp1}
\newlabel{eqn:signs-intro1}{{I-1}{3}}
\newlabel{eqn:signs-intro2}{{I-2}{3}}
\newlabel{eqn:decomp}{{I-3}{3}}
\citation{zhang-97}
\citation{bdp3}
\newlabel{rem:gen}{{2}{4}}
\newlabel{eqn:conj}{{I-4}{4}}
\citation{griffiths}
\citation{clemens}
\citation{ceresa}
\@writefile{toc}{\contentsline {section}{\tocsection {}{1}{Cycles and the Griffiths group}}{5}}
\newlabel{sec:cyc-grif}{{1}{5}}
\citation{harris}
\citation{harris}
\citation{bloch-crelle}
\citation{schoen-duke}
\citation{schoen-tams}
\citation{bdp1}
\citation{bloch-duke}
\citation{bloch-duke}
\citation{bloch-duke}
\citation{bloch-duke}
\citation{nekovar}
\citation{bloch-duke}
\@writefile{toc}{\contentsline {section}{\tocsection {}{2}{Coniveau and the refined Bloch-Beilinson conjecture}}{7}}
\newlabel{sec:con-bb}{{2}{7}}
\newlabel{subsec:refined-conj}{{2.1}{7}}
\@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{2.1}{The refined conjecture}}{7}}
\citation{bloch-kato}
\citation{nekovar-ht}
\newlabel{subsec:AJ}{{2.2}{8}}
\@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{2.2}{Abel-Jacobi}}{8}}
\newlabel{prop:aj-coniveau}{{2.2.1}{8}}
\newlabel{eqn:delta0v}{{2.2.2}{8}}
\@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{2.3}{The Bloch-Kato exponential and logarithm}}{8}}
\newlabel{eqn:cris}{{2.3.1}{8}}
\newlabel{eqn:ss}{{2.3.2}{8}}
\citation{nekovar-ht}
\citation{bloch-kato}
\citation{nekovar}
\citation{katz-messing}
\newlabel{eqn:ext}{{2.3.3}{9}}
\newlabel{eqn:log-alt}{{2.3.4}{9}}
\newlabel{sec:con-hodge}{{2.4}{9}}
\@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{2.4}{Coniveau and the Hodge filtration}}{9}}
\citation{bloch-duke}
\citation{bloch-duke}
\citation{kisin}
\newlabel{prop:coniveau-derham}{{2.4.1}{10}}
\newlabel{cor:coniveau-derham}{{2.4.2}{10}}
\citation{kisin}
\citation{pet-ste}
\citation{bdp2}
\citation{deshalit}
\citation{katz}
\citation{deshalit}
\citation{bdp1}
\citation{bdp2}
\@writefile{toc}{\contentsline {section}{\tocsection {}{3}{$p$-adic $L$-functions}}{12}}
\newlabel{sec:padicL}{{3}{12}}
\newlabel{sec:katz-L}{{3.1}{12}}
\@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{3.1}{The Katz $p$-adic $L$-function}}{12}}
\newlabel{prop:interpolation}{{3.1.1}{12}}
\newlabel{eqn:interpkatz}{{3.1.1}{12}}
\newlabel{sec:p-adic-Rankin-L}{{3.2}{12}}
\@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{3.2}{$p$-adic Rankin $L$-series}}{12}}
\citation{bdp1}
\citation{bdp1}
\citation{bdp2}
\citation{bdp2}
\citation{bdp2}
\citation{bdp1}
\newlabel{eqn:alg-part-rankin}{{3.2.1}{13}}
\newlabel{eqn:defLpRankin}{{3.2.2}{13}}
\newlabel{sec:factor}{{3.3}{13}}
\@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{3.3}{Factorization of the $p$-adic Rankin $L$-series}}{13}}
\newlabel{prop:factor}{{3.3.1}{13}}
\newlabel{eqn:factoring}{{3.3.1}{13}}
\citation{bdp1}
\citation{bdp1}
\citation{bdp1}
\@writefile{toc}{\contentsline {section}{\tocsection {}{4}{Generalized Heegner cycles and coniveau}}{14}}
\newlabel{sec:ghc}{{4.1}{14}}
\@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{4.1}{Generalized Heegner cycles}}{14}}
\newlabel{eqn:cycledefn}{{4.1.1}{14}}
\newlabel{prop:corr}{{4.1.1}{14}}
\newlabel{eqn:PG}{{4.1.2}{14}}
\newlabel{eqn:PD}{{4.1.3}{14}}
\newlabel{eqn:sigmatau}{{4.1.4}{15}}
\citation{bdp1}
\citation{bdp1}
\newlabel{prop:corr-AJ}{{4.1.2}{16}}
\newlabel{eqn:idem}{{4.1.6}{16}}
\newlabel{eqn:AJP}{{4.1.7}{16}}
\newlabel{thm:bdp1}{{4.1.3}{16}}
\citation{bdp1}
\newlabel{sec:fields}{{4.2}{17}}
\@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{4.2}{Fields of definition}}{17}}
\newlabel{eqn:znz}{{4.2.1}{17}}
\newlabel{eqn:defndeltat}{{4.2.2}{17}}
\newlabel{eqn:sigma}{{4.2.3}{17}}
\newlabel{cor:deltat}{{4.2.2}{17}}
\citation{bdp1}
\citation{scholl}
\newlabel{thm:bdp1-new}{{4.2.5}{18}}
\newlabel{sec:cycle-gr}{{4.3}{18}}
\@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{4.3}{Cycles associated with Grossencharacters}}{18}}
\newlabel{eqn:okisom}{{4.3.1}{18}}
\newlabel{eqn:deltatK}{{4.3.2}{18}}
\citation{gs}
\citation{greenberg}
\newlabel{thm:main}{{4.3.1}{19}}
\newlabel{eqn:defn-algpart}{{4.3.3}{19}}
\newlabel{prop:denom}{{4.3.2}{19}}
\newlabel{eqn:lvalue-series}{{4.3.4}{20}}
\newlabel{eqn:coset}{{4.3.6}{20}}
\newlabel{cor:main-explicit}{{4.3.5}{21}}
\@writefile{toc}{\contentsline {section}{\tocsection {}{5}{Miscellany}}{21}}
\newlabel{sec:nonCM}{{5.1}{21}}
\@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{5.1}{A non-CM example}}{21}}
\newlabel{thm:nonCM1}{{5.1.1}{21}}
\newlabel{thm:nonCM2}{{5.1.2}{21}}
\citation{bdp1}
\citation{bdp1}
\citation{katz-CM}
\citation{DR}
\newlabel{eqn:lpneq0}{{5.1.1}{22}}
\newlabel{eqn:dfneq0}{{5.1.2}{22}}
\citation{DR}
\citation{shimura}
\newlabel{rem:non-CM}{{5.1.4}{24}}
\newlabel{sec:fermatquartic}{{5.2}{24}}
\@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{5.2}{The Fermat quartic revisited}}{24}}
\newlabel{eqn:jacobi}{{5.2.1}{25}}
\newlabel{eqn:wei}{{5.2.2}{25}}
\citation{bdp1}
\citation{walds}
\citation{bdp1}
\newlabel{eqn:dfmodp}{{5.2.3}{26}}
\newlabel{eqn:i/4}{{5.2.4}{26}}
\newlabel{eqn:(i-8)/20}{{5.2.5}{26}}
\citation{bdp1}
\citation{gs}
\citation{schappacher}
\@writefile{toc}{\contentsline {section}{\tocsection {Appendix}{A}{Tables}}{28}}
\newlabel{sec:tables}{{A}{28}}
\citation{edixhoven}
\citation{DR}
\citation{DR}
\citation{C}
\citation{C}
\@writefile{toc}{\contentsline {section}{\tocsection {Appendix}{B}{Integrality of modular forms via intersection theory \\ by Brian Conrad }}{30}}
\newlabel{appendix-brian}{{B}{30}}
\@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{B.1}{Introduction}}{30}}
\newlabel{qsec}{{B.1.1}{30}}
\@writefile{toc}{\contentsline {subsubsection}{\tocsubsubsection {}{B.1.1}{Integrality and $q$-expansions}}{30}}
\newlabel{exampleexists}{{B.1.1.1}{30}}
\newlabel{stacksec}{{B.1.2}{30}}
\@writefile{toc}{\contentsline {subsubsection}{\tocsubsubsection {}{B.1.2}{Moduli stacks}}{30}}
\newlabel{moddef}{{B.1.2.1}{30}}
\citation{C}
\citation{DR}
\citation{O}
\citation{C}
\citation{C}
\citation{C}
\citation{C}
\newlabel{omegaU}{{B.1.2.1}{31}}
\@writefile{toc}{\contentsline {subsubsection}{\tocsubsubsection {}{B.1.3}{Results}}{31}}
\citation{DR}
\newlabel{pcase}{{B.1.3.1}{32}}
\@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{B.2}{Intersection-theoretic bounds}}{32}}
\@writefile{toc}{\contentsline {subsubsection}{\tocsubsubsection {}{B.2.1}{Elimination of $q$-expansions}}{32}}
\newlabel{chevfinite}{{B.2.1.1}{32}}
\citation{crt}
\citation{C}
\citation{C}
\citation{KM}
\citation{chinberg}
\citation{chinberg}
\newlabel{intthy}{{B.2.2}{33}}
\@writefile{toc}{\contentsline {subsubsection}{\tocsubsubsection {}{B.2.2}{Divisor and intersection theory formalism}}{33}}
\newlabel{intrel}{{B.2.2.2}{33}}
\citation{ega}
\citation{chinberg}
\newlabel{degreedef}{{B.2.2.3}{34}}
\newlabel{degcurve}{{B.2.2.4}{35}}
\newlabel{degD}{{B.2.2.5}{35}}
\newlabel{dotdef}{{B.2.2.6}{35}}
\newlabel{degLdef}{{B.2.2.1}{35}}
\citation{ega}
\newlabel{intprop}{{B.2.2.7}{36}}
\newlabel{cartier}{{B.2.2.8}{36}}
\newlabel{deltaint}{{B.2.2.2}{37}}
\newlabel{geom}{{B.2.3}{39}}
\@writefile{toc}{\contentsline {subsubsection}{\tocsubsubsection {}{B.2.3}{Geometric calculations}}{39}}
\newlabel{i1}{{B.2.3.1}{39}}
\newlabel{remdeg}{{B.2.3.1}{39}}
\citation{DR}
\newlabel{formula}{{B.2.3.2}{40}}
\newlabel{n=2}{{B.2.3.3}{40}}
\newlabel{muineq}{{B.2.3.2}{40}}
\newlabel{n=3}{{B.2.3.5}{40}}
\citation{C}
\citation{C}
\citation{C}
\citation{KM}
\citation{C}
\citation{KM}
\newlabel{genmod}{{B.3}{41}}
\@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{B.3}{Explicit formulas}}{41}}
\newlabel{numerology}{{B.3.1}{41}}
\@writefile{toc}{\contentsline {subsubsection}{\tocsubsubsection {}{B.3.1}{Numerology for $X_0(N)$}}{41}}
\newlabel{linedeg}{{B.3.1.1}{41}}
\newlabel{lindeg}{{B.3.1.2}{41}}
\newlabel{x0Ngeom}{{B.3.1.3}{41}}
\citation{KM}
\newlabel{intlower}{{B.3.1.4}{42}}
\newlabel{ptorsion}{{B.3.1.5}{42}}
\citation{DR}
\newlabel{gamma0}{{B.3.2}{43}}
\@writefile{toc}{\contentsline {subsubsection}{\tocsubsubsection {}{B.3.2}{Multiplicity bounds for $\Gamma _0(N)$}}{43}}
\newlabel{mainest}{{B.3.2.1}{43}}
\newlabel{matrixint}{{B.3.2.1}{44}}
\newlabel{nuvector}{{B.3.2.2}{45}}
\newlabel{lower}{{B.3.2.3}{45}}
\bibcite{bdp1}{BDP1}
\bibcite{bdp2}{BDP2}
\bibcite{bdp3}{BDP3}
\bibcite{beilinson}{Be}
\bibcite{bloch-crelle}{Bl-1}
\bibcite{bloch-duke}{Bl-2}
\bibcite{bloch-kato}{BK}
\bibcite{ceresa}{Cer}
\bibcite{chinberg}{Ch}
\bibcite{clemens}{Cl}
\bibcite{C}{Co}
\bibcite{DR}{DR}
\bibcite{deshalit}{dS}
\bibcite{edixhoven}{E}
\bibcite{gs}{GS}
\bibcite{greenberg}{Gre}
\bibcite{griffiths}{Gr-1,2}
\bibcite{ega}{EGA}
\bibcite{harris}{Har}
\bibcite{jannsen-banff}{Jan}
\bibcite{katz}{Katz1}
\bibcite{katz-CM}{Katz2}
\bibcite{KM}{KM}
\bibcite{katz-messing}{KMe}
\bibcite{kisin}{Kis}
\bibcite{crt}{Mat}
\bibcite{nekovar}{Nek1}
\bibcite{nekovar-ht}{Nek2}
\bibcite{O}{Ol}
\bibcite{pet-ste}{PS}
\bibcite{schappacher}{Schap}
\bibcite{schoen-duke}{Schoen1}
\bibcite{schoen-tams}{Schoen2}
\bibcite{scholl}{Scholl}
\bibcite{shimura}{Shim}
\bibcite{walds}{Wa}
\@writefile{toc}{\contentsline {section}{\tocsection {Appendix}{}{References}}{46}}
\bibcite{zhang-97}{Zh}
\newlabel{tocindent-1}{0pt}
\newlabel{tocindent0}{58.61125pt}
\newlabel{tocindent1}{66.11127pt}
\newlabel{tocindent2}{31.81927pt}
\newlabel{tocindent3}{0pt}