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Aug 16, 2019 at 15:42 comment added Stefano @StevenSam Thank you! It is exactly what I was looking for!
Aug 16, 2019 at 4:03 comment added Steven Sam @Stefano Yes, the criterion I asked for is not enough for surfaces in characteristics 2 and 3, but one can use etale cohomology to further separate these exotic examples from abelian surfaces. Since this answer helped me with a paper, I'll post it here: arxiv.org/abs/1203.2575 (the reference for what I said is in Remark 3.2).
Aug 15, 2019 at 5:10 comment added Stefano I guess this is a very late comment, but I will try it. In the above, does one actually need the field to be the complex numbers, or could it be any field of characteristic zero?
Aug 8, 2010 at 17:12 vote accept Steven Sam
Aug 8, 2010 at 11:05 history edited damiano CC BY-SA 2.5
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Aug 8, 2010 at 9:56 comment added Pete L. Clark So, just to be sure...**yes**, right?
Aug 8, 2010 at 6:37 history answered damiano CC BY-SA 2.5