This is a graduate-level text on algebraic geometry that provides a
quick and fully self-contained development of the fundamentals,
including all commutative algebra which is used. A taste of the
deeper theory is given: some topics, such as local algebra and
ramification theory, are treated in depth. The book culminates with
a selection of topics from the theory of algebraic curves,
including the Riemann-Roch theorem, elliptic curves, the zeta
function of a curve over a finite field, and the Riemann hypothesis
for elliptic curves.
General
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