Monodromy weight filtration is independent of l

TL;DR

This paper proves that the monodromy weight filtration remains consistent across different primes l for smooth varieties over local fields, enhancing understanding of monodromy in algebraic geometry.

Contribution

It establishes the l-independence of the monodromy weight filtration and the geometric monodromy representation for smooth varieties over local fields.

Findings

Proves l-independence of monodromy weight filtration.

Demonstrates l-independence of geometric monodromy representation.

Enhances understanding of monodromy in algebraic geometry.

Abstract

In this paper, we prove the l-independence of monodromy weight filtration for a geometrically smooth variety over an equicharacteristic local field. We also prove the l-independence for the geometric monodromy representation on the associated graded module of weight monodromy filtration.