Quelques calculs d'espaces $\R^i f_* G$ sur des courbes

TL;DR

This paper investigates properties of the sheaf R^i f_* G associated with affine relative curves over a base scheme, focusing on aspects like cancellation, representability, and stratification.

Contribution

It provides new results on the properties of R^i f_* G for affine relative curves with smooth compactification, especially for solvable groups.

Findings

Establishes cancellation properties of R^i f_* G

Proves representability of the sheaf under certain conditions

Describes stratification of the sheaf in the context of affine curves

Abstract

We give some properties (cancellation, representability, stratification) of the sheaf R^i f_* G for an affine relative curve f:U -> S admitting a smooth compactification and G a solvable group.