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\begin{document}

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\section*{Quasi-Coherent Sheaves and Tannaka Duality Theorems}

\hypertarget{context}{}\subsubsection*{{Context}}\label{context}

\hypertarget{higher_geometry}{}\paragraph*{{Higher geometry}}\label{higher_geometry}

[[!include higher geometry - contents]]

\hypertarget{higher_algebra}{}\paragraph*{{Higher algebra}}\label{higher_algebra}

[[!include higher algebra - contents]]

This page provides links related to

\begin{itemize}%
\item [[Jacob Lurie]], \emph{Quasi-Coherent Sheaves and Tannaka Duality Theorems} (\href{http://www.math.harvard.edu/~lurie/papers/DAG-VIII.pdf}{pdf})

\end{itemize}
On [[quasi-coherent sheaves]] and [[Tannaka duality for geometric stacks]] in the context of [[derived algebraic geometry]] over [[E-infinity rings]] -- [[E-∞ geometry]]

\hypertarget{contents}{}\section*{{Contents}}\label{contents}

\noindent\hyperlink{1_generalities_on_spectral_delignemumford_stacks}{1. Generalities on spectral Deligne-Mumford stacks}\dotfill \pageref*{1_generalities_on_spectral_delignemumford_stacks} \linebreak
\noindent\hyperlink{14_quasicompactness_of_spectral_delignemumford_stacks}{1.4 Quasi-compactness of Spectral Deligne-Mumford stacks}\dotfill \pageref*{14_quasicompactness_of_spectral_delignemumford_stacks} \linebreak
\noindent\hyperlink{2_quasicoherent_sheaves}{2. Quasi-coherent sheaves}\dotfill \pageref*{2_quasicoherent_sheaves} \linebreak
\noindent\hyperlink{21_sheaves_on_a_spectrally_ringed_topos}{2.1 Sheaves on a spectrally ringed $\infty$-topos}\dotfill \pageref*{21_sheaves_on_a_spectrally_ringed_topos} \linebreak
\noindent\hyperlink{22_module_geometries}{2.2 Module geometries}\dotfill \pageref*{22_module_geometries} \linebreak
\noindent\hyperlink{23_quasicoherent_sheaves}{2.3 Quasi-coherent sheaves}\dotfill \pageref*{23_quasicoherent_sheaves} \linebreak
\noindent\hyperlink{24_quasiaffine_spectral_delignemumford_stacks}{2.4 Quasi-affine spectral Deligne-Mumford stacks}\dotfill \pageref*{24_quasiaffine_spectral_delignemumford_stacks} \linebreak
\noindent\hyperlink{25_pullbacks_and_pushforwards_of_quasicoherent_sheaves}{2.5 Pullbacks and pushforwards of quasi-coherent sheaves}\dotfill \pageref*{25_pullbacks_and_pushforwards_of_quasicoherent_sheaves} \linebreak
\noindent\hyperlink{26_local_properties_of_quasicoherent_sheaves}{2.6 Local properties of quasi-coherent sheaves}\dotfill \pageref*{26_local_properties_of_quasicoherent_sheaves} \linebreak
\noindent\hyperlink{27_quasicoherent_sheaves_on_a_functor}{2.7 Quasi-coherent sheaves on a functor}\dotfill \pageref*{27_quasicoherent_sheaves_on_a_functor} \linebreak
\noindent\hyperlink{3_geometric_stacks_and_tannaka_duality}{3. Geometric stacks and Tannaka duality}\dotfill \pageref*{3_geometric_stacks_and_tannaka_duality} \linebreak
\noindent\hyperlink{4_coaffine_stacks}{4. Coaffine stacks}\dotfill \pageref*{4_coaffine_stacks} \linebreak
\noindent\hyperlink{5_tannaka_duality_for_generalized_algebraic_gerbes}{5. Tannaka duality for generalized algebraic gerbes}\dotfill \pageref*{5_tannaka_duality_for_generalized_algebraic_gerbes} \linebreak


\hypertarget{1_generalities_on_spectral_delignemumford_stacks}{}\subsection*{{1. Generalities on spectral Deligne-Mumford stacks}}\label{1_generalities_on_spectral_delignemumford_stacks}

\hypertarget{14_quasicompactness_of_spectral_delignemumford_stacks}{}\subsubsection*{{1.4 Quasi-compactness of Spectral Deligne-Mumford stacks}}\label{14_quasicompactness_of_spectral_delignemumford_stacks}

\begin{example}
\label{}\hypertarget{}{}
\textbf{cor. 1.4.3}

A [[spectral scheme]] or [[spectral Deligne-Mumford stack]], regarded as a [[structured (∞,1)-topos]] is locally coherent.

\end{example}
\hypertarget{2_quasicoherent_sheaves}{}\subsection*{{2. Quasi-coherent sheaves}}\label{2_quasicoherent_sheaves}

\hypertarget{21_sheaves_on_a_spectrally_ringed_topos}{}\subsubsection*{{2.1 Sheaves on a spectrally ringed $\infty$-topos}}\label{21_sheaves_on_a_spectrally_ringed_topos}

\hypertarget{22_module_geometries}{}\subsubsection*{{2.2 Module geometries}}\label{22_module_geometries}

\begin{itemize}%
\item [[tangent (∞,1)-category]]


\item [[geometry (for structured (∞,1)-toposes)]]



\end{itemize}
\hypertarget{23_quasicoherent_sheaves}{}\subsubsection*{{2.3 Quasi-coherent sheaves}}\label{23_quasicoherent_sheaves}

\begin{itemize}%
\item [[quasi-coherent sheaf]]

\end{itemize}
\hypertarget{24_quasiaffine_spectral_delignemumford_stacks}{}\subsubsection*{{2.4 Quasi-affine spectral Deligne-Mumford stacks}}\label{24_quasiaffine_spectral_delignemumford_stacks}

\hypertarget{25_pullbacks_and_pushforwards_of_quasicoherent_sheaves}{}\subsubsection*{{2.5 Pullbacks and pushforwards of quasi-coherent sheaves}}\label{25_pullbacks_and_pushforwards_of_quasicoherent_sheaves}

\begin{itemize}%
\item [[scallop decomposition]]


\item [[Grothendieck context]] [[six operations]]



\end{itemize}
\hypertarget{26_local_properties_of_quasicoherent_sheaves}{}\subsubsection*{{2.6 Local properties of quasi-coherent sheaves}}\label{26_local_properties_of_quasicoherent_sheaves}

\begin{itemize}%
\item [[coherent sheaf]]

\end{itemize}
\hypertarget{27_quasicoherent_sheaves_on_a_functor}{}\subsubsection*{{2.7 Quasi-coherent sheaves on a functor}}\label{27_quasicoherent_sheaves_on_a_functor}

\hypertarget{3_geometric_stacks_and_tannaka_duality}{}\subsection*{{3. Geometric stacks and Tannaka duality}}\label{3_geometric_stacks_and_tannaka_duality}

\hypertarget{4_coaffine_stacks}{}\subsection*{{4. Coaffine stacks}}\label{4_coaffine_stacks}

\hypertarget{5_tannaka_duality_for_generalized_algebraic_gerbes}{}\subsection*{{5. Tannaka duality for generalized algebraic gerbes}}\label{5_tannaka_duality_for_generalized_algebraic_gerbes}

category: reference



\end{document}