Research
My research interests are in stable homotopy theory, tensor-triangular geometry, and their interactions with other areas, in particular, purity and commutative algebra. This page contains a list of my publications and preprints, together with links.
Publications and preprints
| # | Title | Coauthors | References | Links |
|---|---|---|---|---|
| 13 | Definable functors between triangulated categories with applications to tensor‑triangular geometry and representation theory | Isaac Bird | Submitted | arXiv |
| 12 | The homological spectrum via definable subcategories | Isaac Bird | Submitted | arXiv |
| 11 | Tensor‑triangular rigidity in chromatic homotopy theory | Scott Balchin and Constanze Roitzheim | Israel J. Math. (to appear) | arXiv |
| 10 | Finitistic dimensions over commutative DG‑rings | Isaac Bird, Liran Shaul, and Prashanth Sridhar | Math. Z., 309(1): Paper No. 3, 29pp, 2025 | Journal and arXiv |
| 9 | Duality pairs, phantom maps, and definability in triangulated categories | Isaac Bird | Proc. Roy. Soc. Edinburgh Sect. A (to appear) | Journal and arXiv |
| 8 | Local Gorenstein duality in chromatic group cohomology | Luca Pol | J. Pure Appl. Algebra, 227(11):Paper No. 107422, 29pp, 2023 | Journal and arXiv |
| 7 | Levels of algebraicity in stable homotopy theories | Jocelyne Ishak and Constanze Roitzheim | J. Lond. Math. Soc. (2), 108(2):545–577, 2023 | Journal and arXiv |
| 6 | Lifting (co)stratifications between tensor triangulated categories | Liran Shaul | Israel J. Math., 261(1): 249–280, 2024 | Journal and arXiv |
| 5 | Algebraic models of change of groups functors in (co)free rational equivariant spectra | J. Pure Appl. Algebra, 226(11):Paper No. 107108, 53pp, 2022 | Journal and arXiv | |
| 4 | The homotopy theory of complete modules | Luca Pol | J. Algebra, 594:74–100, 2022 | Journal and arXiv |
| 3 | Torsion models for tensor‑triangulated categories: the one‑step case | Scott Balchin, J.P.C. Greenlees, and Luca Pol | Algebr. Geom. Topol., 22(6):2805–2856, 2022 | Journal and arXiv |
| 2 | Flatness and Shipley's algebraicization theorem | Homology Homotopy Appl., 23(1):191–218, 2021 | Journal and arXiv | |
| 1 | The Left Localization Principle, completions and cofree G‑spectra | Luca Pol | J. Pure Appl. Algebra, 224(11):Paper No. 106408, 33pp, 2020 | Journal and arXiv |