Arithmetic duality for two-dimensional local rings with perfect residue field

TL;DR

This paper refines Saito's arithmetic duality for two-dimensional local rings by establishing algebraic group structures on arithmetic cohomology groups, enhancing the understanding of their algebraic properties.

Contribution

It introduces algebraic group structures to arithmetic cohomology groups in two-dimensional local rings, providing a more detailed duality framework.

Findings

Arithmetic duality is refined with algebraic group structures.

Enhanced understanding of cohomology groups in local rings.

Provides a new algebraic perspective on duality theory.

Abstract

We give a refinement of Saito's arithmetic duality for two-dimensional local rings by giving algebraic group structures for arithmetic cohomology groups.