\relax \citation{harris-tschi} \citation{bog-tschi} \citation{hassett-tschi} \@writefile{toc}{\contentsline {section}{\numberline {1}Introduction}{1}} \citation{Beukers1} \citation{Beukers2} \@writefile{toc}{\contentsline {section}{\numberline {2}Generalities}{2}} \newlabel{sect:generalities}{{2}{2}} \@writefile{toc}{\contentsline {subsection}{\numberline {2.1}Integral points}{2}} \citation{vojta} \@writefile{toc}{\contentsline {subsection}{\numberline {2.2}Vojta's conjecture}{3}} \citation{faltings} \citation{vojta-1} \citation{mcquillan} \citation{colliot-swd} \@writefile{toc}{\contentsline {section}{\numberline {3}Geometry}{4}} \newlabel{sect:morphisms}{{3}{4}} \@writefile{toc}{\contentsline {subsection}{\numberline {3.1}Morphisms of pairs}{4}} \newlabel{sect:morphisms-1}{{3.1}{4}} \newlabel{rem:nc}{{3.3}{4}} \citation{colliot-swd} \newlabel{theo:chevalley-weil}{{3.4}{5}} \@writefile{lof}{\contentsline {figure}{\numberline {1}{\ignorespaces The log surface $(X,D)$}}{6}} \newlabel{logsurface1}{{1}{6}} \newlabel{prob:main}{{3.7}{7}} \@writefile{toc}{\contentsline {subsection}{\numberline {3.2}Projective bundles in the \'etale topology}{7}} \newlabel{prob:eee}{{3.10}{8}} \@writefile{toc}{\contentsline {subsection}{\numberline {3.3}Punctured varieties}{8}} \citation{iitaka} \citation{SGA} \citation{iitaka} \newlabel{prob:geom}{{3.11}{9}} \newlabel{prop:nocover}{{3.12}{9}} \citation{hassett-tschi} \citation{serre-MordellWeil} \newlabel{prob:punc}{{3.13}{10}} \@writefile{toc}{\contentsline {section}{\numberline {4}The fibration method and nondegenerate multisections}{10}} \newlabel{sect:fibration}{{4}{10}} \newlabel{prob:nondegenerate}{{4.1}{10}} \citation{noot} \citation{silverman} \citation{masser} \citation{masser1} \citation{serre-MordellWeil} \citation{bombieri-masser-zannier} \citation{harris-tschi} \citation{bog-tschi} \citation{hassett-tschi} \citation{bog-tschi} \citation{harris-tschi} \citation{hassett-tschi} \citation{bog-tschi} \citation{bog-tschi} \newlabel{prop:group}{{4.7}{14}} \newlabel{prop:ellipK3}{{4.8}{14}} \citation{hassett-tschi} \@writefile{toc}{\contentsline {section}{\numberline {5}Approximation techniques}{15}} \newlabel{sect:approx}{{5}{15}} \newlabel{prop:group-punc}{{5.1}{15}} \citation{voskresenskii} \@writefile{toc}{\contentsline {section}{\numberline {6}Conic bundles and integral points}{16}} \newlabel{sect:conic}{{6}{16}} \@writefile{toc}{\contentsline {subsection}{\numberline {6.1}Results on linear algebraic groups}{16}} \newlabel{subsection:gps}{{6.1}{16}} \citation{Ono2} \citation{milne} \citation{Ono1} \citation{Shyr} \citation{GIT} \citation{Beukers1} \@writefile{toc}{\contentsline {subsection}{\numberline {6.2}Group actions and integral points}{18}} \newlabel{prop:groupmodel}{{6.1}{18}} \newlabel{prop:infinitepts}{{6.2}{18}} \newlabel{prop:conicpoints}{{6.3}{18}} \citation{Beukers1} \newlabel{prop:linepoints}{{6.5}{19}} \@writefile{toc}{\contentsline {subsection}{\numberline {6.3}$v$-adic geometry}{19}} \newlabel{subsection:vadic}{{6.3}{19}} \newlabel{prop:etalecase}{{6.6}{20}} \newlabel{prop:doublecase}{{6.7}{20}} \citation{serre-LocalFields} \citation{serre-MordellWeil} \newlabel{eqnsquare}{{1}{21}} \newlabel{prop:hilb}{{6.8}{21}} \newlabel{coro:adicpoints}{{6.9}{22}} \@writefile{toc}{\contentsline {subsection}{\numberline {6.4}A density theorem for surfaces}{22}} \newlabel{rem:ramification}{{6.10}{22}} \newlabel{theo:pelldense}{{6.11}{23}} \@writefile{toc}{\contentsline {subsection}{\numberline {6.5}Cubic surfaces containing a line}{23}} \citation{Beukers2} \citation{Beukers2} \newlabel{rem:realcase}{{6.12}{26}} \newlabel{theo:cubicdense}{{6.13}{26}} \newlabel{coro:BeukersThm2}{{6.14}{26}} \newlabel{coro:BeukersThm1}{{6.15}{26}} \@writefile{toc}{\contentsline {subsection}{\numberline {6.6}Other applications}{27}} \newlabel{theo:P1P1}{{6.17}{27}} \citation{bog-tschi} \citation{silverman-2} \citation{Beukers1} \newlabel{theo:index1}{{6.18}{28}} \@writefile{toc}{\contentsline {section}{\numberline {7}Potential density for log K3 surfaces}{28}} \newlabel{prob:xd}{{7.1}{28}} \citation{Beukers2} \citation{blr} \newlabel{theo:logK3dense}{{7.2}{29}} \@writefile{toc}{\contentsline {subsection}{\numberline {7.1}Appendix: some geometric remarks}{29}} \citation{lehmer} \bibcite{Beukers1}{1} \bibcite{Beukers2}{2} \bibcite{bog-tschi}{3} \bibcite{bombieri-masser-zannier}{4} \bibcite{blr}{5} \bibcite{css-1}{6} \bibcite{colliot-swd}{7} \bibcite{css-3}{8} \bibcite{faltings}{9} \bibcite{SGA}{10} \bibcite{harris-tschi}{11} \bibcite{hassett-tschi}{12} \bibcite{iitaka}{13} \bibcite{KMM}{14} \bibcite{lehmer}{15} \bibcite{mcquillan}{16} \bibcite{masser1}{17} \bibcite{masser}{18} \bibcite{milne}{19} \bibcite{GIT}{20} \bibcite{noot}{21} \bibcite{Ono1}{22} \bibcite{Ono2}{23} \bibcite{serre-AlgGroups}{24} \bibcite{serre-LocalFields}{25} \bibcite{serre-MordellWeil}{26} \bibcite{Shyr}{27} \bibcite{silverman}{28} \bibcite{silverman-2}{29} \bibcite{vojta}{30} \bibcite{vojta-1}{31} \bibcite{voskresenskii}{32}