Timeline for Algorithms for Diophantine Systems
Current License: CC BY-SA 2.5
6 events
| when toggle format | what | by | license | comment | |
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| Sep 4, 2010 at 2:20 | comment | added | Minhyong Kim | Chris: Of course you're right and you understand these matters far better than I do. But it seems to me worth emphasizing occasionally that all one needs for the algorithm to work is not even close to the full BSD, but just the finitness of, say, the 2-primary part of the Tate-Shafarevich group. | |
| Sep 3, 2010 at 17:08 | comment | added | Chris Wuthrich | Correct, there are no algorithms, but there are very good conjectural algorithms for genus 1 curves, i.e. computer programs that will be able to decide if there is a solution (and find them all). If it can't then some conjecture is wrong (BSD). Of course larger examples, say an intersection of 196 quadrics in $\mathhb{P}^{379}$ won't even have that. | |
| Sep 3, 2010 at 17:07 | comment | added | Charles Siegel | Your argument seems to also answer this question: mathoverflow.net/questions/11488/varieties-cut-by-quadrics am I understanding correctly? | |
| Sep 3, 2010 at 17:06 | vote | accept | Charles Siegel | ||
| Sep 3, 2010 at 17:02 | history | edited | David E Speyer | CC BY-SA 2.5 |
added 57 characters in body
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| Sep 3, 2010 at 16:56 | history | answered | David E Speyer | CC BY-SA 2.5 |