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Counting lattices in simple Lie groups: The positive characteristic case

Counting lattices in simple Lie groups: The positive characteristic case

In this article, we prove the following conjecture by Lubotzky. Let G=G0(K), where K is a local field of characteristic p≥5 and where G0 is a simply connected, absolutely almost simple K-group of K-rank at least 2. We give the rate of growth of ρx(G ):=|{Γ⊆G|Γ a lattice in G,vol(G/Γ)≤x}/∼|, …