On the moduli description of ramified unitary Local models of signature (n-1,1)

We give a moduli description for the ramified unitary local model of signature (n-1,1) with any parahoric level structure when the residue field has characteristic not equals 2, confirming a conjecture of Smithling. As applications, we can present moduli descriptions for: (1) ramified unitary Pappas-Zhu local models with any parahoric level; (2) the irreducible components of their special fiber with maximal parahoric level; (3) integral model of ramified unitary Shimura varieties for any (quasi-)parahoric level.