Models and filtrations in tensor triangular geometry

Project

• Lumina quaeruntur project no. LQ100192601

• 01/01/2026  to  31/12/2030

• Grantor: Czech Academy of Sciences

Abstract

The primary goal of this project is to significantly advance the understanding of tensor triangular geometry by exploring models and decompositions associated with filtrations of the Balmer spectrum. This research bridges disciplines by extending the rich theory of tilting objects and derived equivalences — well-established in representation theory and recently expanded in commutative algebra — to the broader setting of tensor triangular geometry. Through this approach, we aim to uncover novel insights in algebraic geometry and extend these findings to other fields within the tensor triangular setting, including equivariant stable homotopy theory. The project leverages the applicant’s extensive expertise in the theory of large (i.e., not finitely generated) representations of commutative and non-commutative rings, which he recently started to apply within tensor triangular geometry. To achieve these ambitious goals, involving leading experts in stable homotopy theory, algebraic geometry, and representation theory is integral to the project.

The team

PI

• Michal Hrbek

Research Fellows

• Leonid Positselski

• Alexandra Zvonareva

Postdocs

• Giovanna Le Gros

• Charalampos Verasdanis

Students

• Daniel Negreiros Lobo

• Simone Pizzirani

Events

Homotopical Methods in Geometry and Representation Theory 

•  15th-19th February 2027, Institute of Mathematics, Czech Academy of Sciences

•  Michal Hrbek, Gustavo Jasso, Fernando Muro, Jan Šťovíček, Alexandra Zvonareva

Visitors

• Sergio Pavon

• Pat Lank

• Rudradrip Biswas

Papers

Preprints

1.      M. Hrbek, J. Hu, R. Zhu. On silting complexes associated to n-silting modules. arXiv preprint arXiv:2602.13794.

2.      L. Positselski. Homomorphisms of topological rings and change-of-scalar functors. arXiv preprint arXiv:2603.15048.

3.      C. Verasdanis. The singularity category of a separable extension. arXiv preprint arXiv:2605.08868.

4.      M. Hrbek, P. Lank, G. Le Gros, S. Pavon. Proxy smallness meets t-structures. arXiv preprint arXiv:2605.26057.

5.      R. Laking, A. Zvonareva. Limits and colimits in silting theory with applications to the wall and chamber structure of an algebra. arXiv preprint arXiv:2605.07555.

6.      D. Herbera, M. Hrbek, G. Le Gros. Semi-Bousfield classes and nonmonotone perversities. arXiv preprint arXiv:2605.30262.

7.      C. Verasdanis. Non-distributive lattices of thick tensor-ideals via trivial extensions. arXiv preprint arXiv:2606.18217.

8.      M. Hrbek, P. Lank, S. Pizzirani. Perfectly generated t-structures for algebraic stacks. arXiv preprint 2506.18803.