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Mar 21, 2020 at 10:16 comment added Evgeny Shinder In Tschinkel's talk maths.ed.ac.uk/cheltsov/edge2017/pdf/yura.pdf, on slide 15 he says that it is a conjecture of Colliot-The'le`ne that existence of a point plus vanishing of Br(X_K)/Br(K) for all field extensions K/k implies stable rationality for del Pezzo surfaces.
May 11, 2016 at 12:32 comment added Daniel Loughran @René: If you want to discuss this approach more, feel free to contact me via email.
May 11, 2016 at 12:23 comment added R.P. Thanks Daniel! The "extra non-rationality criterion" that you mention looks promising, maybe I will look into it later. It should be a finite check, as you suggest.
May 11, 2016 at 9:42 vote accept R.P.
May 11, 2016 at 9:01 history edited Daniel Loughran CC BY-SA 3.0
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May 11, 2016 at 8:33 history answered Daniel Loughran CC BY-SA 3.0