Algebraic Cogroups and Nori-Motives

TL;DR

This paper introduces algebraic cogroups over subfields of complex numbers and demonstrates that all Nori motives over such fields can be represented as quotients of specific motivic cohomology groups, advancing the understanding of motives.

Contribution

It defines algebraic cogroups and proves that every Nori motive is isomorphic to a quotient of a motive of the form H^n(X, Y)(i), providing a new structural insight.

Findings

Every Nori motive over a subfield of complex numbers is a quotient of a motive H^n(X, Y)(i).

Introduction of algebraic cogroups over subfields of complex numbers.

Establishment of a structural characterization of Nori motives.

Abstract

We introduce the notion of algebraic cogroup over a subfield $k$ of the complex numbers, and use it to prove that every Nori motive over $k$ is isomorphic to a quotient of a motive of the form $H^n(X, Y)(i)$.