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The main results of the paper are:
Proposition 0.1. A group G acting coarsely on a coarse space (X,𝓒) induces a coarse equivalence g ↦ g·x₀ from G to X for any x₀ ∈ X.
Theorem 0.2. Two coarse structures 𝓒₁ and 𝓒₂ on the same set X are equivalent if the following conditions are satisfied:
(1) Bounded sets in 𝓒₁ are identical with bounded sets in 𝓒₂.
(2) There is a coarse action ϕ₁ of a group G₁ on (X,𝓒₁) and a coarse action ϕ₂ of a...
We investigate the structure of the Tukey ordering among directed orders arising
naturally in topology and measure theory.
The aim of these notes is to generalize Laumon’s construction [20] of automorphic sheaves
corresponding to local systems on a smooth, projective curve to the case of local
systems with indecomposable unipotent ramification at a finite set of points. To this end
we need an extension of the notion of parabolic structure on vector bundles to coherent
sheaves. Once we have defined this, a lot of arguments from the article “ On the
geometric Langlands conjecture” by Frenkel, Gaitsgory and Vilonen [11]...
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