Analyse micro-locale l-adique en caracteristique p > 0: Le cas d’un trait, math
- A. Abbes, T. Saito
0.1. A perfect complex P of R-modules yields a homotopy point [P ] of the K-theory spectrum K(R). The Euler characteristics, i.e., the class χ(P ) of P in K0(R) = π0K(R), is the connected component where [P ] lies, so [P ] can be considered as an “animation” of χ(P ). When R is commutative, the determinant sends the fundamental groupoid of K(R) to the groupoid L(R) of graded super R-lines; this is a morphism of the Picard groupoids (see [Del3]), so [P ] controls, in particular, the determinant line detP . The local Riemann-Roch story, as seen in [Del3] and [Gr], unfolds within these grounds.