Abstract Let X be an algebraic curve with a faithful action of finite group G over field k . We show that if the Hodge–de Rham short exact sequence splits -equivariantly then on is weakly ramified. In particular, this generalizes result Köck and Tait for hyperelliptic curves. discuss also converse statements tie problem to lifting coverings curves ring Witt vectors length 2.

Let $\widetilde{X}$ be a smooth Riemannian manifold equipped with proper, free, isometric and cocompact action of discrete group $\Gamma$. In this paper we prove that the analytic surgery exact sequence Higson-Roe for is isomorphic to associated adiabatic deformation Lie groupoid $\widetilde{X}\times_\Gamma\widetilde{X}$. We then generalize result context smoothly stratified manifolds. Finally,...