\contentsline {section}{\tocsection {}{1}{Background and motivation}}{1}
\contentsline {section}{\tocsection {}{2}{Hida families and periods for weight one forms}}{6}
\contentsline {section}{\tocsection {}{3}{Generalized Kato classes}}{9}
\contentsline {subsection}{\tocsubsection {}{3.1}{Definition}}{9}
\contentsline {subsection}{\tocsubsection {}{3.2}{Basic properties}}{11}
\contentsline {subsection}{\tocsubsection {}{3.3}{Enhanced regulators}}{14}
\contentsline {subsection}{\tocsubsection {}{3.4}{The conjecture}}{15}
\contentsline {section}{\tocsection {}{4}{Special cases}}{16}
\contentsline {subsection}{\tocsubsection {}{4.1}{Beilinson-Kato classes}}{16}
\contentsline {subsection}{\tocsubsection {}{4.2}{Belinson-Flach classes}}{17}
\contentsline {subsection}{\tocsubsection {}{4.3}{Complex multiplication classes and Heegner points}}{18}
\contentsline {subsubsection}{\tocsubsubsection {}{4.3.1}{The rank $(1,1)$ setting}}{19}
\contentsline {subsubsection}{\tocsubsubsection {}{4.3.2}{The rank $(2,0)$ setting}}{20}
\contentsline {subsection}{\tocsubsection {}{4.4}{Real multiplication classes and Stark-Heegner points}}{21}
\contentsline {subsection}{\tocsubsection {}{4.5}{Adjoint classes}}{22}
\contentsline {subsubsection}{\tocsubsubsection {}{4.5.1}{The rank $(0,2)$ setting}}{23}
\contentsline {subsubsection}{\tocsubsubsection {}{4.5.2}{The rank $(1,1)$ setting}}{23}
\contentsline {subsubsection}{\tocsubsubsection {}{4.5.3}{The rank $(2,0)$ setting}}{23}
\contentsline {section}{\tocsection {}{}{References}}{24}