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\begin{document}
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\begin{center}

  \huge{The Department of Mathematics}\\[0.1\baselineskip]
  \Large{2016--17--B term}\\[0.2\baselineskip]

\end{center}

\begin{description}
  \item[Course Name]
    Derived categories IV

  \item[Course Number]
    \LRE{201‭.2‭.0364}

  \item[Course web page]\mbox{}\\
    \url{https://www.math.bgu.ac.il/~amyekut/teaching/2016-17/der-cats-IV/course_page.html}

  \item[Lecturer]
    Prof. Amnon Yekutieli,
    \nolinkurl{<amyekut@bgu.ac.il>},
    Office 202

\item[Office Hours]
  \url{https://www.math.bgu.ac.il/en/teaching/hours}
\end{description}

\section*{Abstract}




\section*{Requirements and grading\footnote{Information may change during the first two weeks of the term. Please consult the webpage for updates}}




    \includepdf[pages=-]{advert-dercats-IV.pdf}



\section*{Course topics}

Topics:

\begin{enumerate}
\item{} Rigidity, residues and duality over commutative rings. We will study rigid residue
complexes. We will prove their uniqueness and existence, the trace and localization
functoriality, and the ind-rigid trace homomorphism.
\item{} Derived categories in geometry. This topic concerns geometry in the wide sense.
We will prove existence of K-flat and K-injective resolutions, and talk about derived
direct and inverse image functors.
\item{} Rigidity, residues and duality over schemes. The goal is to present an accessible
approach to global Grothendieck duality for proper maps of schemes. This approach
is based on rigid residue complexes and the ind-rigid trace. We will indicate a generalization of this approach to DM stacks.
\item{} Derived categories in noncommutative ring theory. Subtopics: dualizing complexes, tilting complexes, the derived Picard group, derived Morita theory, survey of
noncommutative and derived algebraic geometry.
\end{enumerate}

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