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Feb 17, 2013 at 10:29 comment added user28172 The $H^1(k,X)$ in this answer should be $H^1(k,{\rm{Aut}}_{X/k})$ (and one should note the relevance of projectivity hypotheses to ensure effectivity of descent, unless "object" is understood in some sense like algebraic spaces).
Feb 17, 2013 at 9:59 vote accept Jérémy Blanc
Feb 17, 2013 at 6:04 comment added Will Sawin Does this suffice?
Feb 17, 2013 at 6:03 history edited Will Sawin CC BY-SA 3.0
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Feb 17, 2013 at 0:44 comment added Jérémy Blanc Thx. By "precise description" I really meant something precise, like diagonal tori or matrices of the form [a,b*mu, b,a], with some conditions on a,b.
Feb 16, 2013 at 14:26 comment added Ben Webster Yes, the description is in Aakumadula's comment above.
Feb 16, 2013 at 11:01 comment added Jérémy Blanc Thx Will. So in my case I have just GL_2(Z), which is Z/2Z. Does this helps to get a precise description of the tori?
Feb 16, 2013 at 6:44 history answered Will Sawin CC BY-SA 3.0