ERC Starting Grant - RationAlgic

**Duration:**** **** **01.04.2021 - 31.03.2026

**Volume:**** **1 498 750 Euro

**Abstract:**** **** **Algebraic Geometry has one of the longest histories among all branches of mathematics with some of its roots dating back to the work of the Hellenistic Greeks from the 5th century B.C. The EU-funded "RationAlgic" project addresses some classical problems and questions in this area via a mix of modern methods and theories. One central question is the rationality problem, that is, the question whether (almost all) solutions of a given polynomial equation in several variables can be uniquely parametrized by rational functions. Another important aspect is the study of algebraic cycles, which roughly amounts to the question which subvarieties a given variety has. Both of these topics are closely intertwined with each other. An important technical tool that we will use for both questions is unramified cohomology.