Good Reductions of Shimura Varieties of Hodge Type in Arbitrary Unramified Mixed Characteristic, Part II

TL;DR

This paper proves Milne's conjecture on the existence of integral canonical models for Shimura varieties of abelian type in unramified mixed characteristic, and confirms a related motivic conjecture for p=2.

Contribution

It establishes the existence of integral canonical models for a broad class of Shimura varieties and verifies Milne's motivic conjecture for p=2.

Findings

Proves Milne's conjecture on integral canonical models in unramified mixed characteristic.

Confirms Milne's motivic conjecture for p=2 for Shimura varieties of Hodge type.

Advances understanding of the structure and models of Shimura varieties.

Abstract

We prove a conjecture of Milne pertaining to the existence of integral canonical models of Shimura varieties of abelian type in arbitrary unramified mixed characteristic $(0,p)$. As an application we prove for $p=2$ a motivic conjecture of Milne pertaining to integral canonical models of Shimura varieties of Hodge type.