On the conductor formula of Bloch

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Wild ramification and the characteristic cycle of an ℓ-adic sheaf (2007, methodology): “1 For the convenience of a reader familiar with the terminologies on log geometry as in [12] §4, we include a lemma, not used in the sequel, showing that the Definition 1.”
The logarithmic cotangent complex (2005, background): “In fact, the beginnings of a theory of log cotangent complexes can be found in the recent work of K. Kato and T. Saito ([ 12 ]) on logarithmic localized intersection product, where it is used to study a proper scheme over a complete discrete valuation ring whose reduced closed fiber is a divisor wit”
On the crystalline period map (2011, background): “lly log complete intersection map. Then (1.9.1) yields quasi-isomorphisms (1.9.2) LΩ· (Z,M)/(S,L)/F m→∼ Rulog Z/S∗(O /J [m] ). Proof. (a) Let f : (Z,M) →(S,L) be a map of ﬁne log schemes. Recall (see [KS] 4.4.2, 4.4.4 or [Ol1] 6.8) that fis locally log complete intersection map if ´etale locally it ”