Timeline for Brauer-Manin obstruction and Tate-Shafarevich group of an Abelian variety
Current License: CC BY-SA 2.5
9 events
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| Jan 12, 2010 at 12:24 | history | edited | Chandan Singh Dalawat | CC BY-SA 2.5 |
Added the reference to Skorobogatov.
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| Jan 11, 2010 at 4:13 | comment | added | Chandan Singh Dalawat | @Felipe : You are right. It is perhaps expected to be true for curves of genus >1. | |
| Jan 10, 2010 at 15:13 | comment | added | Felipe Voloch | @Chandan This has not been proved for curves, only for torsors of abelian varieties. | |
| Jan 10, 2010 at 14:55 | vote | accept | CommunityBot | moved from User.Id=19475 by developer User.Id=69903 | |
| Jan 10, 2010 at 14:55 | |||||
| Jan 10, 2010 at 13:26 | comment | added | Chandan Singh Dalawat | Strictly speaking, there is no obstruction whatsoever to the existence of rational point on an abelian variety : the origin is a rational point ! What you have in mind is that if C is smooth projective curve of genus >0 with jacobian J, or if C is a torsor under an abelian variety J, everything being defined over some number field K, and if C has K_v-points at every place v of K, then the Manin obstruction to the existence of a K-point is the only one as long as Sha(J) is finite. | |
| Jan 10, 2010 at 12:57 | comment | added | Chandan Singh Dalawat | You might be especially interested in Theorème 4.1 in Harari's article. | |
| Jan 10, 2010 at 12:54 | history | edited | Chandan Singh Dalawat | CC BY-SA 2.5 |
added 398 characters in body
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| Jan 10, 2010 at 12:49 | comment | added | user19475 | For reference: I. Manin, "Le groupe de Brauer-Grothendieck en géométrie diophantienne", Proc. Internat. Congr. Math. (Nice), 1970. | |
| Jan 10, 2010 at 12:42 | history | answered | Chandan Singh Dalawat | CC BY-SA 2.5 |