Ramified class field theory and duality over finite fields

2021/04/07 by Gupta, Rahul, Krishna, Amalendu
#19E15 #Algebraic Geometry (math.AG) #FOS: Mathematics #Primary 14C25 #Secondary 14F42

paper · doi:10.48550/arxiv.2104.03029

Abstract

We prove a duality theorem for the p-adic etale motivic cohomology of a variety U which is the complement of a divisor on a smooth projective variety over \F_p. This extends the duality theorems of Milne and Jannsen-Saito-Zhao. The duality introduces a filtration on H¹_\etl(U, \Q/\Z). We identify this filtration to the classically known Matsuda filtration when the reduced part of the divisor is smooth. We prove a reciprocity theorem for the idele class groups with modulus introduced by Kerz-Zhao and Rulling-Saito. As an application, we derive the failure of Nisnevich descent for Chow groups with modulus.

Related

• Geometric class field theory with bounded ramification
• On Kato's ramification filtration
• Duality for integral motivic cohomology
• Weil-étale Cohomology over p-adic Fields
• On the structure of etale motivic cohomology