Prove the arithmetic Siu inequality for general adelic curves

Prove the arithmetic Siu inequality in the setting of general adelic curves, in order to extend height equidistribution for divisors beyond the Cartier-divisor case.

Background

The paper seeks a height-equidistribution identity for two nef adelic line bundles on a projective variety over a non-archimedean globally valued field. Existing arguments over global fields use the arithmetic Siu inequality to compare heights of divisors and to remove restrictions on the divisor presentation.

The authors note that an extension of the relevant equidistribution result to adelic curves exists under stronger assumptions, but the standard approach requires an arithmetic Siu inequality that has not been established for general adelic curves. They consequently derive the needed height identity by proving an arithmetic Hodge index theorem and related intersection inequalities for globally valued fields.