The logarithmic cotangent complex

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p-adic periods and derived de Rham cohomology (2011, background): “of dg algebras; same in the relative situation. Examples. (a) For a ﬁnite extension K′ of K, consider the pair Spec(K′,OK′ ). The log scheme Spec(K′,O K′ ) is a log complete intersection over OK (see [O] 6.8). If πis a generatorof OK′/OK, f(t) its minimal polynomial, then, by [O] 6.9, L (K′,O K′) is”
Logarithmic Stable Maps (2008, background): “9 in [28], we obtain an A-module exact sequence 0 → AutI(C † ×S† W )→ RelDef(f) = Rπ∗f TW †/S† ⊗OS I → Def(f) → DefI(C † ×S† W ) φ → RelOb(f) = R(1)π∗f TW †/S† ⊗OS I → Ob(f)→ 0”
On the crystalline period map (2011, methodology): “true, by the direct limit argument, if (Z,M) is projective limit of log (S,L)-schemes (Zα,Mα) as in the theorem with respect to a directed family of aﬃne transition maps. (ii) In the original theorem [Ol1] 6.10, Olsson uses his version of log cotangent complex; there fneed not be integral. For integ”
p-adic derived de Rham cohomology (2012, methodology): “be calculated using any projective resolution as these are all homotopy equivalent. Remark 6.4. Gabber’s cotangent complex complex Lf from Deﬁnition 6.3 is denoted LG f in [Ols05, §8]. The same paper [Ols05] also introduces a different version of the cotangent complex for a morphism of ﬁne log schem”
Logarithmic Geometry and Moduli (2010, background): “([49], 3.”