A Proof of the Absolute Purity Conjecture (after Gabber)

183 citations recorded by the source corpus.

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

Cohomological Hasse principle and motivic cohomology for arithmetic schemes (2010, background): “homology theory H´et(−,Λ) in Example 1.4. The last fact follows from the purity isomorphism Rai!Λ(1) = ˆ Λ 0 a = 2 a 6= 2 where i : s →S is the closed immersion. By the absolute purity due to Gabber ([FG], see also [SS, Lemma 1.8]), for X ∈CS which is integral regular with dimS(X) = d, we have (1.8)”
WEIGHT SPECTRAL SEQUENCES AND INDEPENDENCE OF $\ell$ (2003, background): “We further identify RHom(ΛD[−1],Λ(1)) with ΛD[−1] by the isomorphism ΛD → RiΛ(1)[2] defined by the fundamental class of D [7].”
A finiteness theorem for zero-cycles over p-adic fields (2006, methodology): “tting of δ: H2d Xs(X,Λ(d)) ≃H 2d− ´et (Xs,Λ(d−1)) ≃H 2d− ´et (X,Λ(d−1)) −→j∗ H2d−2 ´et (Xη,Λ(d−1)) −−→∪[π] H2d ´et (Xη,Λ(d)), where the ﬁrst isomorphism follows from the purity theorem of Gabber (cf. [Fu]) and the second from the proper base change theorem and the last map is given by the cup produc”