Cherlin–Zilber Algebraicity Conjecture

Establish that every infinite simple group of finite Morley rank is isomorphic to a simple algebraic group over an algebraically closed field.

Background

Groups of finite Morley rank arise naturally in model theory as binding groups and admit a well-behaved notion of dimension (Morley rank). A central goal in the area is to show that such groups coincide with classical algebraic groups when they are simple, thereby bridging model-theoretic and algebraic structures.

This conjecture has been a driving force in the field since the pioneering work of Zilber and Cherlin and underpins many classification programs for groups of finite Morley rank.