Motivic Intersection Complex of Certain Shimura varieties

TL;DR

This paper shows that for specific Shimura varieties, the motivic intersection complex aligns with motivic weight truncation, ensuring a unique, well-defined intermediate extension satisfying Wildeshaus's criteria.

Contribution

It establishes the equivalence of motivic intersection complex and weight truncation for certain Shimura varieties, extending Wildeshaus's framework.

Findings

Motivic intersection complex matches weight truncation in specified cases.

Ensures the motivic intersection complex is uniquely defined.

Satisfies Wildeshaus's intrinsic characterization for intermediate extensions.

Abstract

Using a version of weight conservativity we demonstrate that for certain Shimura varieties (including all Shimura three-folds, most Shimura four-folds and the Siegel sixfold) the construction of the motivic intersection complex due to Wildeshaus compares with a motivic weight truncation in the sense of S. Morel. In particular it is defined up to a unique isomorphism, and satisfies the intrinsic characterization for an intermediate extension due to Wildeshaus.