Pontryagin duality for varieties over $p$-adic fields

Abstract

We define cohomological complexes of locally compact abelian groups associated with varieties over $p$-adic fields and prove a duality theorem under some assumption. Our duality takes the form of Pontryagin duality between locally compact motivic cohomology groups.

New definition of cohomology of strict normal crossing schemes (section 3), and cohomology of schemes with such reduction (section 4.3). Improved exposition in several places

References in corpus (2)

• Higher Topos Theory
• Homological algebra with locally compact abelian groups