Arithmetic duality theorems for 1-motives over function fields
Cristian D. Gonzalez-Aviles
TL;DR
This paper extends duality theorems for 1-motives from number fields to function fields and establishes a Poitou-Tate exact sequence for finite flat group schemes over global function fields.
Contribution
It introduces a Poitou-Tate exact sequence for finite flat group schemes and generalizes duality theorems for 1-motives to the setting of function fields.
Findings
Established a Poitou-Tate exact sequence for finite flat group schemes
Extended duality theorems for 1-motives to function fields
Unified duality results across number fields and function fields
Abstract
In this paper we obtain a Poitou-Tate exact sequence for finite and flat group schemes over a global function field. We also extend the duality theorems for 1-motives over number fields obtained by D.Harari and T.Szamuely to the function field case.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Polynomial and algebraic computation · Meromorphic and Entire Functions