WEIGHT SPECTRAL SEQUENCES AND INDEPENDENCE OF $\ell$

By Takeshi Saito. Journal of the Institute of Mathematics of Jussieu, 2003

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On the conductor formula of Bloch (2004, methodology): “Theorem 6.3.1.1 is a consequence of Theorem 1 of [ 41 ].”
Good reduction criterion for K3 surfaces (2014, result): “ero modulo torsion. Proposition 2.3. Let Xbe as in the previous proposition (with no assumption on charK). Let l6=pbe a prime. Let Λ be Z/lnZ, Zl, or Ql. 3 This numbering is the same to that of Saito [SaiT03]. Some authors (e.g. [RZ82], [Mok93], [Ill94]) write −(p+1) for this space. 4 This liftabili”
Local-global compatibility and the action of monodromy on nearby cycles (2010, background): “e In this section, we will explain a way of writing down explicitly the monodromy ﬁltration on the complex of nearby cycles RψΛ, in the case of a semistable scheme. Our exposition will follow that of [Sa2], which constructs the monodromy ﬁltration using perverse sheaves. We let Λ = Z/lrZ,Zl,Ql or Q¯”
Miscellany on traces in ℓ-adic cohomology: a survey (2006, background): “(2) By taking A= uf −1 ,B= f , 8.1 slightly improves T. Saito’s lemma 2.3 in [ S3 ], because we assume rationality only for the traces of uf n , not for the traces of the u m f n .”