×

Ramification and cleanliness (joint work with Takeshi Saito). (English) Zbl 1264.14028

Let \(K\) be a perfect field of characteristic \(p>0\), \(X\) be a smooth,separated and quasi-compact \(K\)-scheme, \(D\) be a simple normal crossing divisor on \(X\), \(U:=X-D.\) Let also \(l\) be a fixed prime \(l \neq p\), a finite local \(\mathbb Z_{l}\)-algebra \(\Lambda\) and \(\mathcal{F}\) be a locally constant constructible sheaf of \(\Lambda\)-modules on \(U\). The paper under review is a report of an extended article [joint work with T. Saito, “Ramification and cleanliness”, arXiv:1007.3873], concerning a geometrical approach of the problem of describing the ramification of \(\mathcal{F}\) along \(D\) and giving a Riemann-Roch type conjectural formula for \(\mathcal{F}\). The work is part of a series of papers of the two authors concerning the study of the ramification of Galois torsors and of \(l\)-adic sheaves in characteristic \(p>0\) with \(l \neq p\).

MSC:

14F20 Étale and other Grothendieck topologies and (co)homologies
11S15 Ramification and extension theory
PDFBibTeX XMLCite