Leveled sub-cohomology

TL;DR

This paper introduces a new functor called leveled sub-cohomology, based on leveled cycles on smooth projective varieties, aiming to uncover structural insights related to levels in algebraic geometry.

Contribution

It defines a novel functor that connects leveled cycles with cohomological structures, expanding the understanding of levels in algebraic geometry.

Findings

Defines the leveled sub-cohomology functor

Establishes a connection between leveled cycles and cohomology

Provides a framework for exploring level structures in varieties

Abstract

In this paper we define a functor-- leveled sub-cohomology. (It bears no relation with the level of elliptic curves). It is based on leveled cycles on a smooth projective variety, and will be expected to reveal a structure in the level.