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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10$\begingroup$ 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. $\endgroup$– Dan PetersenCommented Mar 20, 2012 at 9:23
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$\begingroup$ Alright. I will. $\endgroup$– HarryCommented Mar 20, 2012 at 9:39
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2$\begingroup$ Over nonperfect fields there are nontrivial torsors for unipotent groups, e.g., Exercise (3), top of p. 130, Serre's "Galois Cohomology" $\endgroup$– Jason StarrCommented Mar 20, 2012 at 11:00
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2$\begingroup$ Just adding to Jason's comment that over perfect fields the torsors are indeed trivial. $\endgroup$– ShripadCommented Mar 20, 2012 at 12:28
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2$\begingroup$ 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. $\endgroup$– Jason StarrCommented Mar 20, 2012 at 13:16
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