Mathematical publications, preprints, and notes

Here is a list of my papers and preprints (in an order that makes sense from some perspective).
  1. Support theory via actions of tensor triangulated categories, arXiv:1105.4692 (J. Reine Angew. Math. 681 (2013) 219-254);
  2. Subcategories of singularity categories via tensor actions, arXiv:1105.4698 ( Compos. Math. 150 (2014) 229-272);
  3. On the derived category of a graded commutative noetherian ring, with I. Dell'Ambrogio, arXiv:1107.4764 (J. Algebra 373 (2013) 356-376).
  4. A note on thick subcategories of stable derived categories, with H. Krause, arXiv:1111.2220 (Nagoya Math. J. 212 (2013) 87-96);
  5. Even more spectra: tensor triangular comparison maps via graded commutative 2-rings, with I. Dell'Ambrogio, arXiv:1204.2185 (Appl. Categ. Structures 22 (2014) 169-210);
  6. Filtrations via tensor actions, arXiv:1206.2721 (Int. Math. Res. Not. 2018 (2018) no. 8 2535-2558);
  7. Duality for bounded derived categories of complete intersections, arXiv:1206.2724 (Bull. Lond. Math. Soc. 46 (2014), no. 2, 245-257)
  8. appendix to: D. Benson, S. Iyengar, H. Krause, Module categories for group algebras over commutative rings, arXiv:1208.1291 (J. K-theory 11 (2013) 297-329)
  9. Derived categories of absolutely flat rings, arXiv:1210.0399 (Homology Homotopy Appl. 16 (2014), no. 2, 45-64)
  10. The derived category of a graded Gorenstein ring, with J. Burke, arXiv:1507.00830 ("Commutative algebra and noncommutative algebraic geometry (II)", Math. Sci. Res. Inst. Publ., 68 (2015), pp. 93-123)
  11. Strong generators in tensor triangulated categories, with J. Steen, arXiv:1409.0645 (Bull. Lond. Math. Soc. 47 (2015) 607-616)
  12. Derived categories of representations of small categories over commutative noetherian rings, with B. Antieau, arXiv:1507.00456 (Pacific J. Math. 283 (2016), no. 1, 21-42)
  13. Gorenstein homological algebra and universal coefficient theorems, with I. Dell'Ambrogio and J. Stovicek, arXiv:1510.00426 (Math. Z. 287 (2017) no. 3-4 1109-1155)
  14. The prime spectra of relative stable module categories, with S. Baland and A. Chirvasitu, arXiv:1511.03164 (to appear in Trans. Amer. Math. Soc.);
  15. The local-to-global principle for triangulated categories via dimension functions, arXiv:1601.01205 (J. Algebra 473 (2017) 406-429);
  16. A tour of support theory for triangulated categories through tensor triangular geometry, arXiv:1601.03595 (chapter in "Building Bridges Between Algebra and Topology" Advanced courses in mathematics - CRM Barcelona);
  17. Comparisons between singularity categories and relative stable categories of finite groups, with S. Baland, arXiv:1601.07727;
  18. Enrichment and representability for triangulated categories, with J. Steen, arXiv:1604.00880 (to appear in Doc. Math. 22 (2017) 1031-1062);
  19. On the graded dual numbers, arcs, and non-crossing partitions of the integers, with S. Gratz, arXiv:1611.02070;
  20. The frame of smashing tensor-ideals, with P. Balmer and H. Krause, arXiv:1701.05937;
  21. Morita theory and singularity categories, with J.P.C.Greenlees, arXiv:1702.07957;
  22. Tensor-triangular fields I: Ruminations, with P. Balmer and H. Krause, arXiv:1707.02167;
  23. Complete Boolean algebras are Bousfield lattices, arXiv:1707.06007;
  24. The derived category of the projective line, with H. Krause, arXiv:1709.01717;
  25. Homotopy invariants of singularity categories, with S. Gratz, arXiv:1803.06144;
Below one can find, in no particular order, some other things I have written or am in the process of writing.
• My Ph.D. thesis
- written under the supervision of Amnon Neeman at the Australian National University. The results from my thesis, some in a slightly stronger form, appear in papers 1 and 2.
• A proof that if one can make the cone construction in a triangulated category functorial then the category in question is close to being abelian. This fact probably is, or at least should be, well known; a reference can be found in Verdier's thesis (although Verdier assumes the existence of countable products or coproducts).
• A defunct preprint proving that in a compactly generated tensor triangulated category the collection of Bousfield classes forms a set.
This note shows that one can generalise the proof of Ohkawa's theorem due to Dwyer and Palmieri to any compactly generated triangulated category. It was superseded by a more general result of Iyengar and Krause.