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Results tagged with elliptic-curves
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user 3545
An elliptic curve is an algebraic curve of genus one with some additional properties. Questions with this tag will often have the top-level tags nt.number-theory or ag.algebraic-geometry. Note also the tag arithmetic-geometry as well as some related tags such as rational-points, abelian-varieties, heights. Please do not use this tag for questions related to ellipses; instead use conic-sections.
11
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1
answer
847
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Can local duality for elliptic curves be proven with "big rings"?
From Exercise 5.14, Ch. V of Silverman's "Advanced Topics in the Arithmetic of Elliptic Curves", I learned that the local duality for elliptic curves over $p$-adic fields can be proven for Tate curves …
- 13.3k
2
votes
Persistent homology of $\mathbb{F}_p$-points of elliptic curves
I think that going all the way to barcodes and persistent homology is a big leap, and probably not one where there will be something interesting. But maybe there are interesting things if you just go …
- 13.3k
8
votes
1
answer
943
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Where do nonstandard elliptic curve angles come from?
This is a question which has bounced around my head over the past few years. At the same time, I am answering Riemann hypothesis for zeta function of algebraic curves over fields of infinite characte …
- 13.3k
35
votes
Accepted
Is there a "Basic Number Theory" for elliptic curves?
I don't think that such a survey paper or textbook exists, but the closest thing I know of is "A note on height pairings, Tamagawa numbers, and the Birch and Swinnerton-Dyer conjecture" by Spencer Blo …
- 13.3k
11
votes
Accepted
Is there a canonical height on the Weil-Chatelet group?
In my opinion, instead of a "height" on the Weil-Chatelet group, one should consider a "depth", using the local duality between the points on an elliptic curve and the elements of the Weil-Chatelet gr …
- 13.3k
26
votes
0
answers
554
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Elliptic analogue of primes of the form $x^2 + 1$
I have a project in mind for an undergraduate to investigate next quarter -- a curiosity really, but I'm surprised I can't find it in the literature. I do not want a detailed analysis here... but ple …
- 13.3k