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%%%%%% Math 273 Homework \#3, Fall 2010 %%%%%%
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%%%%%% Instructor: Ezra Miller %%%%%%
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\title{\mbox{}\\[-8ex]Math 273 Homework \#3, Fall 2010\\\normalsize
Instructor: Ezra Miller}
\author{Solutions by: ...your name...\\[2ex]
Collaborators: ...list those with whom you worked on this assignment...\\[1ex]}
\date{Due: Thursday 14 October 2010}
\maketitle
\vspace{-3ex}%
\noindent
\textsc{Reading assignments} in \cite{vakil}\vspace{-.5ex}
\begin{itemize}
\item%
by Thursday 30 September: Chapter~6 (should be mostly review)\vspace{-1ex}
\item%
by Tuesday 5 October: Chapter~12, \S13.1--\S13.3; this plus Chapter~6
is a lot of material, but most of it is review (skip any item
mentioning morphisms of schemes)\vspace{-1ex}
\item%
by Thursday 7 October: \S7.1--\S7.3\vspace{-1ex}
\item%
by Thursday 14 October: The rest of Chapter~7\vspace{-1ex}
\item%
by Thursday 21 October: \S8.1 and \S8.3; review \S8.2
\end{itemize}
\noindent
\textsc{Exercises}:
In \cite{vakil}, exercises have labels C.S.N, for ``Chapter~C,
Section~S, Exercise~N'', where $\text{C},\text{S} \in \ZZ_+$ and
$\text{N} \in \text{A},\ldots,\text{Z}$. It is not expected that
everyone will complete all of the assigned exercises, but those marked
``[required]'' are essential.\vspace{-1ex}%
\begin{enumerate}
\item[5.5.B][required---and it's not that tricky]%
\item[5.5.C]%
\item[5.5.F]%
\item[5.5.K][required]%
\item[6.1.B][required]%
\item[6.2.A]%
\item[6.2.D]%
\item[6.3.C]%
\item[6.3.D]%
\item[6.3.E][required]%
\item[6.4.H]%
\item[6.5.B]%
\item[7.2.E][required]%
\item[7.3.E][required]%
\item[7.3.F][required]%
\item[7.3.J]%
\end{enumerate}
Additional exercise.
\begin{enumerate}
\item\mbox{}[required] %
Prove that a scheme $X$ is quasiseparated if and only if the
intersection of any two affine open subsets is a finite union of
affine open subsets.
\end{enumerate}
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\bibitem[Vakil]{vakil}
Ravi Vakil, \emph{Foundations of algebraic geometry}, notes dated
August 26, 2010.
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