# An improvement of the duality formalism of the rational etale site

## TL;DR

This paper enhances the duality formalism of the rational etale site, simplifying proofs and making the framework more accessible, with future applications to duality in two-dimensional local rings.

## Contribution

It introduces an improved duality formalism for the rational etale site that avoids complex approximation arguments, streamlining existing duality theorems.

## Key findings

- Simplified proofs of duality theorems
- Elimination of exotic approximation arguments
- Foundation for future duality studies in local rings

## Abstract

We improve the arithmetic duality formalism of the rational etale site. This improvement allows us to avoid some exotic approximation arguments on local fields with ind-rational base, thus simplifying the proofs of the previously established duality theorems in the rational etale site and making the formalism more user-friendly. In a subsequent paper, this new formulation will be used in a crucial way to study duality for two-dimensional local rings.