On the structure of dg-categories of relative singularities

Non-commutative nature of $\ell$-adic vanishing cycles

“…Recall from [25] that we have the following explicit models for D b coh (G t ) and D b coh (t). The simplicial algebra K O L , (π K , π K ) corresponds, under the Dold-Kan equivalence, to the dg algebra (also denoted K O L , (π K , π K ) , by abuse of notation)…”

“…Morphisms in this category will be written vertically. Notice that it suffices to consider an object in D sg (G t ) represented by some (E, d, [25,Theorem 2.7]): In this case, using the strict models above, one computes that a * 2 a 2 * E → E is…”