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Recommended text.
Silverman, The arithmetic of elliptic curves.
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Course Content.
This course is motivated by the topic of elliptic curves,
especially from the point of view of algebraic geometry. We will start by
doing a quick overview of the theory of elliptic curves, from various
aspsects, including the complex analytic viewpoint and applications
to cryptography. Then we shall cover some of the algebraic geometry
that we shall need, including non-singular curves, divisors,
differentials, Riemann-Roch theorem, etc. (all for varieties), and discuss
some of the finer theory of elliptic curves. If time permits, we will
also discuss the topics of the previous sentence from the viewpoint of
schemes, including sheaf cohomology and Serre duality, which implies the
Riemann-Roch theorem. The prerequisite for this course is a basic graduate
algebra sequence such as GRV I and II. For the scheme-theoretic part (if
we get to it), the prerequisite is either the Algebraic geometry course
taught in Fall 2008 or permission of the instructor.
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Grading.
The grade will be based on homeworks and class attendance.
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Honor Code. The Academic Honor System at The Florida State
University is based on the premise that each student has the
responsibility 1) to uphold the highest standards of academic
integrity in the student's own work, 2) to refuse to tolerate
violations of academic integrity in the University community, and
3) to foster a high sense of integrity and social responsibility
on the part of the University community. A copy of the University
Academic Honor Code can be found in the current Student Handbook
and you are bound by it in all your academic work.
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American Disabilities Act. Students with disabilities needing
academic accommodations should register with and provide documentation
to the Student Disability Resource Center (SDRC), and bring a letter
from the SDRC to the instructor indicating their needs.This should
be done within the first week of class.
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