Hilbert's Tenth Problem over Rings of Integers of Number Fields (Term Paper for Thomas Scanlon's Math 229, Model Theory; December 18, 2006)
The goal of this survey is to understand Bjorn Poonen's theorem about
elliptic curves and Hilbert's Tenth problem over rings of integers of number fields and to
record and exposit a few ideas which may be useful in an attack with
Poonen's theorem as
a starting point.
Lecture Notes
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My notes
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Course title (link to course page)
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Lecturer(s)
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Semester
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Additional Resources
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(pdf)
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Moduli of Surfaces |
BAGS: the joint Harvard/MIT Baby Algebraic geometry
seminar
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Fall 2007
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(pdf)
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Finite Groups in Number Theory |
Lectures by Serre |
Fall 2007
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I (will soon) provide the source for most of my notes for a couple of reasons.
- Somebody might download all my notes, correct the errors and unclear presentation, and then send them back to me. It's not likely, but it could happen.
- If a bomb drops on my house and I lose all my stuff, maybe somebody can give me a copy of my notes.
- The source is much faster to download and compile if you're on a slow connection.
- Personally I appreciate being able to view the tex files of other
people, and if I do use someone's notes for a course or seminar I like to have a
local copy that I can modify, search quickly, format as I wish, etc.
This part of this page (and in fact most of my TeXing abilities and conventions, and
reasons 1-3 above) have
been shamelessly copied from Anton
Gerashenko, who has a whole bunch of goodies on his page.
Also (again paraphrased from Anton), if you see a typo it is trivial to
correct it so please let me know! And if you see a genuine
mathematical error it would be immoral to not correct it, so please let me
know.
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NSF
In the interest of repeating myself less, I made an NSF GRF advice page.
Check these out too.
Why Everyone Should Know Number Theory
The Rising Sea
