note on homework
William Stein
I wanted to add a parenthetical remark to the bottom of one of the
homework problems.
\item In the section of the textbook called {\em Modular forms as
functions on lattices} we define maps between the set $\cR$ of
lattices in $\C$ and the set $\cE$ of isomorphism classes of pairs
$(E,\omega)$, where $E$ is an elliptic curve over $\C$ and $\omega\in
\Omega^1_{E}$ is a nonzero holomorphic differential $1$-form on $E$.
Prove that the maps in each direction defined in the book are
bijections. (See Appendix A1.1 of Katz's {\em $p$-adic properties
of modular schemes and modular forms}.)
That paper by Katz is here:
http://wstein.org/5canz/was/people/katz/katz-p-adic_properties_of_modular_schemes_and_modular_forms.pdf
--
William Stein
Professor of Mathematics
University of Washington
http://wstein.org