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AG (Algebraic geometry)
Pure
See also Sheaf cohomology, Weil cohomology, Flat homology
Totaro referred to flat cohomology as “just a version of étale cohomology”.
Scholl: The ‘p^n’ Selmer group of an elliptic curve over Q can be expressed (essentially) as ‘H^1(Spec Z, E)’, flat cohomology with coeffs in the ‘p^n’ torsion of a Neron model for E.
http://mathoverflow.net/questions/10501/flat-cohomology-and-picard-groups
http://mathoverflow.net/questions/94783/what-is-your-picture-of-the-flat-topology
http://mathoverflow.net/questions/117229/etale-site-is-useful-examples-of-using-the-small-fppf-site
nLab page on Flat cohomology