Poincar\'e duality in logarithmic motivic homotopy theory

TL;DR

This paper establishes Poincaré duality within logarithmic motivic homotopy theory, demonstrating its implications for crystalline cohomology's independence from log compactification choices.

Contribution

It adapts existing arguments to the log setting, proving Poincaré duality for smooth projective morphisms in this framework.

Findings

Proves Poincaré duality in logarithmic motivic homotopy theory.

Shows crystalline cohomology independence from log compactification.

Extends classical duality results to the logarithmic setting.

Abstract

By adapting arguments of Annala-Hoyois-Iwasa in the log setting, we prove Poincar\'e duality for smooth projective morphisms in logarithmic motivic homotopy theory. As an application, we show that the crystalline cohomology of a log compactification is independent of the choice.