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Dec 7, 2016 at 17:23 vote accept David C
Nov 5, 2016 at 19:00 answer added ACL timeline score: 11
Nov 5, 2016 at 15:57 answer added R. van Dobben de Bruyn timeline score: 13
Nov 5, 2016 at 14:36 answer added Donu Arapura timeline score: 8
Nov 5, 2016 at 14:02 comment added R. van Dobben de Bruyn Also, the Brauer group is a birational invariant of smooth projective varieties, which Artin and Mumford use in the second half of their article to reinterpret and generalise the results of the first half.
Nov 5, 2016 at 13:57 comment added R. van Dobben de Bruyn The spaces $H^0(X,\Omega^i_X)$ and $H^i(X,\mathcal O_X)$ are birational invariants in arbitrary characteristic! (The former is an exercise in Hartshorne, and the latter follows in characteristic $0$ from Hodge symmetry, and in characteristic $p$ from a paper by Chatzistamatiou and Rülling.)
Nov 5, 2016 at 11:52 comment added Piotr Achinger the fundamental group is another example
Nov 5, 2016 at 11:30 history asked David C CC BY-SA 3.0