Classifying approximable algebras

TL;DR

This paper investigates the structure of approximable algebras, showing they are subalgebras of section rings of infinite sums of Weil divisors, expanding understanding beyond previous limitations.

Contribution

It demonstrates that approximable algebras, unlike earlier believed, are subalgebras of section rings of infinite sums of Weil divisors, not just of big line bundles.

Findings

Approximable algebras are subalgebras of section rings of infinite sums of Weil divisors.

They are not necessarily subalgebras of section rings of big line bundles.

This expands the structural understanding of approximable algebras.

Abstract

Approximable algebras were defined by Chen in his proof of the Fujita theorem in the arithmetic context. These were shown to not be necessarily subalgebras of section rings of big line bundles in a previous prepreint of the author. Here, we show that whilst approximable algebras are not necessarily subalgebras of section rings of big line bundles, they are necessarily subalgebras of section rings of infinite sums of Weil divisors.