# 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.

## Key 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.

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Source: https://tomesphere.com/paper/1705.00789