ERC Starting Grant · 2021
Spectral Geometry of Higher Categories
The overarching goal of this project is to reveal and systematically study the geometry of important categories in homotopy theory, algebraic geometry, and representation theory. To this end, we will introduce and develop the framework of higher Zariski geometry in which commutative rings are replaced by ring-like categories as the fundamental objects. The resulting theory simultaneously generalizes modern algebraic geometry, derived algebraic geometry as studied by Lurie and Toën--Vezzosi, as well as Balmer's tensor triangular geometry, while introducing entirely new global objects and methods. In particular, it provides a canonical spectral decomposition of a large class of higher…
From the public funding record at EU CORDIS. Describes the funded project, not the reviews below.