The Hodge-D-Conjecture fora Product of Elliptic Curves

TL;DR

This paper proves the Hodge-D-conjecture for general products of elliptic curves up to dimension 5 and reduces the problem to a computable matrix rank condition for higher dimensions.

Contribution

It establishes the Hodge-D-conjecture for products of elliptic curves up to dimension 5 and formulates a computational approach for higher dimensions.

Findings

Hodge-D-conjecture proven for dim X ≤ 5

Reduction to matrix rank condition for dim X ≥ 6

Computational method proposed for higher-dimensional cases

Abstract

Let $X/C$ be a general product of elliptic curves. Our goal is to establish the Hodge-D-conjecture for $X$. We accomplish this when $\dim X \leq 5$. For $\dim X \geq 6$, we reduce the conjecture to a matrix rank condition that is amenable to computer calculation.