On tea, donuts and non-commutative geometry

TL;DR

This paper explores the analogy between enjoying tea and donuts and the mathematical principles of non-commutative geometry, specifically illustrating the relationship between elliptic curves and non-commutative tori through algebraic explanations.

Contribution

It provides an accessible explanation of Serre's Theorem in non-commutative geometry and establishes a novel connection between elliptic curves and non-commutative tori.

Findings

Elliptic curves are shown to be complementary to non-commutative tori.

The algebraic structure underlying Serre's Theorem is elucidated.

A new perspective on the relationship between classical and non-commutative geometry is proposed.

Abstract

As many will agree, it feels good to complement a cup of tea by a donut or two. This sweet relationship is also a guiding principle of non-commutative geometry known as Serre Theorem. We explain the algebra behind this theorem and prove that elliptic curves are complementary to the so-called non-commutative tori.