On the relative twist formula of \(\ell\)-adic sheaves. (English) Zbl 1455.14040
Summary: We propose a conjecture on the relative twist formula of \(\ell\)-adic sheaves, which can be viewed as a generalization of Kato-Saito’s conjecture. We verify this conjecture under some transversal assumptions. We also define a relative cohomological characteristic class and prove that its formation is compatible with proper push-forward. A conjectural relation is also given between the relative twist formula and the relative cohomological characteristic class.
MSC:
| 14F20 | Étale and other Grothendieck topologies and (co)homologies |
| 11G25 | Varieties over finite and local fields |
| 11S40 | Zeta functions and \(L\)-functions |
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