\relax 
\citation{BDP1}
\@writefile{toc}{\contentsline {section}{\tocsection {}{}{Introduction}}{1}}
\citation{kato}
\citation{kolyvagin}
\citation{rubin}
\citation{perrin-riou}
\citation{colmez-bourbaki1}
\citation{colmez-bourbaki2}
\citation{mazur-rubin}
\citation{serre-padic}
\citation{serre-padic}
\@writefile{toc}{\contentsline {section}{\tocsection {}{1}{Classical examples}}{3}}
\newlabel{sec:classical-es}{{1}{3}}
\newlabel{sec:circular-units}{{1.1}{3}}
\@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{1.1}{Circular units}}{3}}
\newlabel{eqn:eisenstein-series}{{1}{3}}
\newlabel{eqn:ordinary-p-stabilisation}{{2}{3}}
\newlabel{eqn:padic-family}{{3}{3}}
\newlabel{eqn:padic-family-0}{{5}{3}}
\citation{katz-interpolation-real}
\newlabel{eqn:siegel-unit}{{6}{4}}
\newlabel{eqn:siegel-unit-p-adic}{{7}{4}}
\newlabel{eqn:gauss-sum}{{8}{4}}
\newlabel{eqn:hchi-logs}{{9}{4}}
\newlabel{eqn:h-chi}{{10}{4}}
\newlabel{thm:leopoldt}{{1.1}{4}}
\newlabel{eqn:E0-chi}{{11}{4}}
\newlabel{eqn:shapiro}{{12}{6}}
\newlabel{eqn:logeta}{{13}{6}}
\citation{kato}
\citation{colmez-bourbaki1}
\citation{perrin-riou-KL}
\citation{perrin-riou-KL}
\newlabel{eqn:leopoldt-bis}{{14}{7}}
\newlabel{eqn:logketa}{{15}{7}}
\newlabel{eqn:leopoldt-bis-log}{{16}{7}}
\newlabel{eqn:exp-dual}{{17}{7}}
\newlabel{eqn:leopoldt-bis-exp-dual}{{18}{7}}
\newlabel{sec:elliptic-units}{{1.2}{8}}
\@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{1.2}{Elliptic units}}{8}}
\newlabel{eqn:eisenstein-H}{{19}{8}}
\newlabel{eqn:heegner-hypothesis}{{20}{8}}
\newlabel{eqn:def-chi-fn}{{21}{8}}
\newlabel{eqn:def-tau-n}{{22}{8}}
\newlabel{eqn:Eisenstein-K}{{23}{8}}
\newlabel{eqn:homogeneity-katz}{{24}{9}}
\newlabel{eqn:algebraicity}{{25}{9}}
\newlabel{eqn:def-tau-np}{{26}{10}}
\newlabel{eqn:p-adic-interpolation-K}{{27}{10}}
\newlabel{eqn:def-Lp-katz-1}{{28}{10}}
\newlabel{thm:katz}{{1.2}{10}}
\newlabel{eqn:k1-k2-L-value}{{29}{11}}
\newlabel{eqn:shimura-maass}{{30}{11}}
\citation{BDP1}
\citation{DR1}
\citation{hida}
\citation{BDP1}
\newlabel{eqn:shimura-algebraicity}{{31}{12}}
\newlabel{eqn:algebraicity-bis}{{32}{12}}
\newlabel{eqn:comparison-delta-d}{{33}{12}}
\newlabel{eqn:fourier-coeffs}{{34}{13}}
\newlabel{eqn:p-depletion-eu}{{35}{13}}
\newlabel{eqn:p-depletion-eu-bis}{{36}{13}}
\newlabel{eqn:p-adic-interpolation-K-bis}{{37}{13}}
\newlabel{thm:katz-bis}{{1.3}{13}}
\citation{Hi88b}
\citation{BDP1}
\citation{BDP1}
\newlabel{sec:heegner-points}{{1.3}{15}}
\@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{1.3}{Heegner points}}{15}}
\newlabel{eqn:comparison-delta-d-bis}{{38}{15}}
\newlabel{eq:phi}{{39}{15}}
\citation{BDP1}
\newlabel{eq:explicit-Lalg-C}{{40}{16}}
\newlabel{eqn:deplete}{{41}{16}}
\newlabel{eq:defLp}{{42}{16}}
\newlabel{eq:f-family}{{43}{16}}
\newlabel{eq:explicit-Lp}{{44}{16}}
\citation{BDP1}
\newlabel{thm:bdp1}{{1.4}{17}}
\newlabel{eq:explicit-Lp-at0}{{45}{17}}
\newlabel{eq:Phi=pV}{{46}{17}}
\citation{kato}
\citation{howard}
\citation{Chor}
\newlabel{eq:BK}{{47}{18}}
\@writefile{toc}{\contentsline {section}{\tocsection {}{2}{Euler systems of Garrett-Rankin-Selberg type}}{19}}
\newlabel{sec:garrett-es}{{2}{19}}
\citation{mtt}
\citation{beilinson}
\citation{Bes-k2}
\citation{BD1}
\newlabel{sec:beilinson-kato}{{2.1}{20}}
\@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{2.1}{Beilinson-Kato elements}}{20}}
\newlabel{eqn:dlog}{{48}{20}}
\citation{BD1}
\newlabel{eqn:drho}{{49}{21}}
\newlabel{eqn:regp}{{50}{21}}
\newlabel{e:uchidef}{{51}{21}}
\newlabel{eqn:petersson}{{52}{21}}
\newlabel{e:etafah}{{53}{21}}
\citation{BD1}
\citation{brunault}
\citation{kato}
\citation{bannai-kings}
\citation{niklas}
\citation{BD1}
\citation{mtt}
\citation{BD1}
\citation{shimura76}
\newlabel{thm:main-bk}{{2.1}{22}}
\citation{BD1}
\newlabel{eqn:shimura}{{54}{23}}
\newlabel{eqn:value(2,2)}{{55}{23}}
\newlabel{eqn:factorisation-rankin}{{56}{23}}
\citation{Bes-syn}
\citation{kato}
\citation{brunault}
\citation{kato}
\citation{BD2}
\citation{BD1}
\newlabel{eqn:comp}{{57}{24}}
\newlabel{eqn:comp-regulators}{{58}{24}}
\newlabel{eqn:main-bk-bis}{{59}{24}}
\citation{brunault}
\citation{perrin-riou-ec}
\citation{colmez-bourbaki1}
\citation{perrin-riou-ec}
\citation{BDR1}
\newlabel{eqn:equivalences}{{60}{25}}
\newlabel{eqn:bsd}{{61}{25}}
\newlabel{sec:beilinson-flach}{{2.2}{25}}
\@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{2.2}{Beilinson-Flach elements}}{25}}
\citation{BDR1}
\newlabel{e:shim}{{63}{26}}
\newlabel{e:tamedef}{{64}{26}}
\newlabel{e:bfdef}{{65}{26}}
\citation{BDR1}
\citation{besser-K1S}
\citation{BDR1}
\newlabel{e:critvals}{{66}{27}}
\newlabel{e:regpk1}{{67}{27}}
\newlabel{t:bdr1}{{2.7}{27}}
\citation{besser-K1S}
\citation{llz}
\citation{BDR2}
\citation{dasgupta}
\citation{citro}
\citation{llz}
\citation{BDR1}
\citation{BDR2}
\newlabel{e:lprankin(2,2)}{{68}{28}}
\citation{BDR2}
\citation{DR1}
\newlabel{sec:gross-kudla}{{2.3}{29}}
\@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{2.3}{Gross-Kudla-Schoen cycles}}{29}}
\citation{HT}
\citation{DR1}
\citation{HT}
\citation{Gar}
\citation{HaKu}
\citation{DR1}
\citation{YZZ}
\citation{GrKu}
\citation{GrSc}
\newlabel{LpHT}{{69}{30}}
\citation{Bes-inv}
\citation{Bes-inv}
\citation{Bes-inv}
\citation{Bes-inv}
\newlabel{AJs}{{70}{31}}
\newlabel{AJpBes}{{71}{31}}
\newlabel{AJpBes2}{{72}{31}}
\newlabel{thm:main-gk}{{2.8}{31}}
\citation{DR1}
\citation{DR1}
\citation{Bes-inv}
\citation{Lau}
\newlabel{formula.main-gk}{{73}{32}}
\newlabel{AJformula}{{74}{32}}
\newlabel{computable}{{75}{32}}
\citation{DR2}
\citation{Zh2}
\citation{DRS1}
\citation{DRS1}
\newlabel{Zhpoint}{{76}{33}}
\citation{DR2}
\citation{DR2}
\newlabel{bigclass}{{78}{34}}
\newlabel{crist}{{79}{34}}
\newlabel{mainBSD-kudla}{{2.9}{34}}
\citation{BDP1}
\citation{BDP1}
\citation{kato}
\citation{brunault}
\citation{niklas}
\citation{BD1}
\citation{BDR1}
\citation{DR1}
\citation{BDP1}
\citation{DR1}
\citation{perrin-riou-GZ}
\citation{BDP1}
\citation{DR1}
\@writefile{toc}{\contentsline {section}{\tocsection {}{}{Conclusion}}{35}}
\bibcite{BD1}{BD1}
\bibcite{BD2}{BD2}
\bibcite{BDP1}{BDP}
\bibcite{BDR1}{BDR1}
\bibcite{BDR2}{BDR2}
\bibcite{beilinson-K1S}{Bei1}
\bibcite{beilinson}{Bei2}
\bibcite{Bes-inv}{Bes1}
\bibcite{Bes-syn}{Bes2}
\bibcite{Bes-k2}{Bes3}
\@writefile{toc}{\contentsline {section}{\tocsection {}{}{References}}{36}}
\bibcite{besser-K1S}{Bes4}
\bibcite{bannai-kings}{BK}
\bibcite{brunault}{Br}
\bibcite{Chor}{Cas}
\bibcite{citro}{Cit}
\bibcite{coleman-bu}{Col}
\bibcite{colmez-bourbaki1}{Cz1}
\bibcite{colmez-bourbaki2}{Cz2}
\bibcite{DR1}{DR1}
\bibcite{DR2}{DR2}
\bibcite{DRS1}{DRS1}
\bibcite{dasgupta}{Das}
\bibcite{GrKu}{GrKu}
\bibcite{GrSc}{GrSc}
\bibcite{Gar}{Gar}
\bibcite{HaKu}{HaKu}
\bibcite{HT}{HaTi}
\bibcite{Hi88b}{Hi1}
\bibcite{hida}{Hi2}
\bibcite{howard}{How}
\bibcite{kato}{Kato}
\bibcite{katz-interpolation-real}{Katz}
\bibcite{kolyvagin}{Ko}
\bibcite{Lau}{Lau}
\bibcite{llz}{LLZ}
\bibcite{mazur-rubin}{MR}
\bibcite{mtt}{MTT}
\bibcite{niklas}{Nik}
\bibcite{perrin-riou-GZ}{PR1}
\bibcite{perrin-riou-ec}{PR2}
\bibcite{perrin-riou}{PR3}
\bibcite{perrin-riou-KL}{PR4}
\bibcite{rubin}{Ru}
\bibcite{serre-padic}{Se}
\bibcite{shimura76}{Sh1}
\bibcite{shimura}{Sh2}
\bibcite{YZZ}{YZZ}
\bibcite{Zh2}{Zh}
\newlabel{tocindent-1}{0pt}
\newlabel{tocindent0}{15.01373pt}
\newlabel{tocindent1}{20.88867pt}
\newlabel{tocindent2}{34.5pt}
\newlabel{tocindent3}{0pt}