# On p-adic comparison theorems for rigid analytic varieties, I

## TL;DR

This paper establishes p-adic comparison theorems for smooth rigid analytic varieties, linking their etale and de Rham cohomologies using syntomic methods and Hyodo-Kato theory, without requiring good integral models.

## Contribution

It introduces a new approach to compute p-adic etale cohomology of rigid varieties via differential forms, expanding the scope beyond existing models.

## Key findings

- Computed p-adic etale cohomology in a stable range
- Constructed Hyodo-Kato cohomology and isomorphism with de Rham cohomology
- Extended p-adic comparison theorems to broader classes of varieties

## Abstract

We compute, in a stable range, the arithmetic p-adic etale cohomology of smooth rigid analytic and dagger varieties (without any assumption on the existence of a nice integral model) in terms of differential forms using syntomic methods. The main technical input is a construction of a Hyodo-Kato cohomology and a Hyodo-Kato isomorphism with de Rham cohomology.