The motive of a smooth Theta divisor

TL;DR

This paper establishes a motivic Lefschetz hyperplane theorem for smooth ample divisors on Abelian varieties and constructs a motive representing their primitive cohomology.

Contribution

It introduces a motivic version of the Lefschetz theorem and constructs a specific motive for primitive cohomology of smooth Theta divisors.

Findings

Proves a motivic Lefschetz hyperplane theorem for Theta divisors.

Constructs a motive realizing primitive cohomology.

Advances understanding of motives in algebraic geometry.

Abstract

We prove a motivic version of the Lefschetz hyperplane theorem for a smooth ample divisor $\Theta$ on an Abelian variety. We use this to construct a motive $P$ that realizes the primitive cohomology of $\Theta$.