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I might have misunderstood something I heard somewhere.

Are torsors over unipotent groups trivial?

I couldn't find this in some standard references.

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Dear Harry, I don't mean to be rude, but you have really been asking a flurry of questions these last few days! I would suggest both that you mull questions over in your mind and search the literature a bit more before asking here (it builds character), and that you make sure to take the time to digest the answers you have received. – Dan Petersen Mar 20 '12 at 9:23
Alright. I will. – Harry Mar 20 '12 at 9:39
Over nonperfect fields there are nontrivial torsors for unipotent groups, e.g., Exercise (3), top of p. 130, Serre's "Galois Cohomology" – Jason Starr Mar 20 '12 at 11:00
Just adding to Jason's comment that over perfect fields the torsors are indeed trivial. – Shripad Mar 20 '12 at 12:28
Also an expert reminded me that, if one allows non-smooth "unipotent" groups and torsors in the fppf topology rather than the etale topology, then there are many other examples. – Jason Starr Mar 20 '12 at 13:16

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