I am currently a Humboldt postdoctoral fellow working in the BIREP group at the Universität Bielefeld.
Below it is possible to find some information about me and my research. Some further information can also be found in my
My email address is gstevens[at]math[dot]uni-bielefeld[dot]de
My research interests
Very briefly (and broadly): Triangulated categories, (noncommutative) algebraic geometry, representation theory, homological algebra
Slightly less briefly: A large component of my research focuses on triangulated categories (as well as various enhancements) and their applications in algebraic geometry and
representation theory. I am particularly interested in classification problems for thick and localizing subcategories, and in extracting
information about related geometric or algebraic objects from such structural results. Lately I've been thinking about singularity
categories, complete intersections and their noncommutative analogues, tensor triangular geometry, bounds on generation time in triangulated categories, and derivators.
Mathematical publications, preprints, and notes
Here is a list of my papers and preprints, in chronological order.
Below one can find, in no particular order, some other things I have written or am in the process of writing.
- Support theory via actions of tensor triangulated categories, arXiv:1105.4692 (J. Reine Angew. Math. 681 (2013) 219-254);
- Subcategories of singularity categories via tensor actions, arXiv:1105.4698 (to appear in Compositio Mathematica);
- On the derived category of a graded commutative noetherian ring, with I. Dell'Ambrogio,
arXiv:1107.4764 (J. Algebra 373 (2013) 356-376).
- A note on thick subcategories of stable derived categories, with H. Krause,
arXiv:1111.2220 (to appear in Nagoya Mathematical Journal);
- Even more spectra: tensor triangular comparison maps via graded commutative 2-rings, with I. Dell'Ambrogio,
arXiv:1204.2185 (to appear in Applied Categorical Structures);
- Filtrations via tensor actions, arXiv:1206.2721;
- Duality for bounded derived categories of complete intersections, arXiv:1206.2724
- 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)
- Derived categories of absolutely flat rings, arXiv:1210.0399
- • 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 short note on amusing examples of Bousfield lattices.
- The purpose of this note is to illustrate that one should not try to prove certain facts about the Bousfield lattice in too much
generality. It turns out that any complete Boolean algebra is the Bousfield lattice of a compactly generated algebraic tensor triangulated
category and that one can use the Bousfield lattice to construct the Booleanisation of a complete Heyting algebra.
- • 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.