Smoothness of moduli space of stable torsion-free sheaves with fixed determinant in mixed characteristic

الأصل · EN

Let R be a complete discrete valuation ring with fraction field of characteristic 0 and algebraically closed residue field of characteristic p>0. Let Xᵣ → Spec(R) be a smooth projective morphism of relative dimension 1. We prove that, given a line bundle Lᵣ the moduli space of Gieseker stable torsion-free sheaves of rank r≥ 2 over Xᵣ, with determinant Lᵣ, is smooth over R.