On weight truncations in the motivic setting

TL;DR

This paper develops a motivic analogue of weight truncation functors using punctual gluing of t-structures, enabling the construction of motivic intersection complexes and the recovery of invariants of singularities.

Contribution

It introduces a new method for weight truncation in motivic sheaves and constructs motivic intersection complexes for threefolds over any field.

Findings

Constructed motivic weight truncation functors.

Built a canonical motivic intersection complex for threefolds.

Recovered invariants of singularities motivically.

Abstract

Using punctual gluing of $t$-structures, we construct an analogue of S. Morel's weight truncation functors (for certain weight profiles) in the setting of motivic sheaves. As an application we construct a canonical motivic analogue of the intersection complex for an arbitrary threefold over any field $k$. We are also able to recover certain invariants of singularities motivically.