Integral models of Shimura varieties with parahoric level structure

For a prime p > 2 , we construct integral models over p for Shimura varieties with parahoric level structure, attached to Shimura data ( G , X ) of abelian type, such that G splits over a tamely ramified extension of 𝐐 p . The local structure of these integral models is related to certain “local models”, which are defined group theoretically. Under some additional assumptions, we show that these integral models satisfy a conjecture of Kottwitz which gives an explicit description for the trace of Frobenius action on their sheaf of nearby cycles.