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Results tagged with arithmetic-geometry
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user 1826
Diophantine equations, rational points, abelian varieties, Arakelov theory, Iwasawa theory.
7
votes
Which curves have infinitely many rational points
Dear Tim:
How right you are to worry about computing the Jacobian of a genus one curve! Years ago, in the midst of many discussions with Bill McCallum, Alex Perlis, Nick Shepherd-Barron, and John T …
- 13.6k
31
votes
Why should I believe the Mordell Conjecture?
Since summer is here, I will bore people a bit with my own ahistorical view
of Mordell. The main point is that Serge Lang's strategy, mentioned by several people, is
essentially correct. Nevertheless …
- 13.6k
150
votes
2
answers
21k
views
What is a Frobenioid?
Since there will be a long digression in a moment, let me start by reassuring you that my intention really is to ask the question in the title.
Recently, there has been a flurry of new discussion sur …
- 13.6k
25
votes
What is an étale theta function?
Update (27 December, 2015): A number of corrections have been made in the two linked PDF documents below,
Update (15 December, 2015): I note that Brian Conrad has written a thoughtful summary avail …
- 13.6k
77
votes
1
answer
15k
views
What is an étale theta function?
Let me start out by urging you to take seriously that whatever I write about the papers surrounding IUTT really are questions. If you would like to use it as a guide to the mathematics in any way, the …
- 13.6k
31
votes
Why certain diophantine equations are interesting (and others are not) ?
Added 22, October:
While reflecting on this question and the subsequent discussion, I fell again into a
bit of a sermonizing mood. I hope I will be forgiven for inserting two words of
caution.
The …
- 13.6k