Publications
Papers
Serre-duality for Tails(A), Proc. Amer. Math. Soc. 125 (1997), 709-716.
Non-commutative graded homological identities, J. London Math. Soc. (2) 57 (1998), 336-350.
Local cohomology for non-commutative graded algebras, Comm. Algebra 25 (1997), 575-591.
Non-commutative Castelnuovo-Mumford regularity, Math. Proc. Cambridge Phil. Soc. 125 (1999), 203-221.
Brown Representability for stable categories, Math. Scand. 85 (1999), 195-218.
Properties of AS-Cohen-Macaulay algebras, J. Pure Appl. Algebra 138 (1999), 239-249.
Gorenstein homomorphisms of non-commutative rings, J. Algebra 211 (1999), 240-267.
Intersection theory on non-commutative surfaces, Trans. Amer. Math. Soc. 352 (2000), 5817-5854.
With James Zhang: Gourmet's Guide to Gorensteinness, Adv. Math. 151 (2000), 313-345.
Spectra of modules, J. Algebra 244 (2001), 744-784.
Triangulated functors, homological functors, tilts, and lifts, Manuscripta Math. 110 (2003), 381-406.
Non-commutative curves and their zeta functions, J. Algebra Appl. 1 (2002), 175-199.
With Anders Frankild: Foxby equivalence, complete modules, and torsion modules, J. Pure Appl. Algebra 174 (2002), 135-147.
With Anders Frankild: Affine equivalence and Gorensteinness, Math. Scand. 95 (2004), 5-22.
With Anders Frankild: Gorenstein Differential Graded Algebras, Israel J. Math. 135 (2003), 327-353.
With Anders Frankild and Srikanth Iyengar: Dualizing Differential Graded modules and Gorenstein Differential Graded Algebras, J. London Math. Soc. (2) 68 (2003), 288-306.
With Anders Frankild: Homological identities for Differential Graded Algebras, J. Algebra 265 (2003), 114-135.
Linear free resolutions over non-commutative algebras, Compositio Math. 140 (2004), 1053-1058.
Recognizing dualizing complexes, Fund. Math. 176 (2003), 251-259.
Auslander-Reiten theory over topological spaces, Comment. Math. Helv. 79 (2004), 160-182.
The Auslander-Reiten quiver of a Poincaré duality space, Algebr. Represent. Theory 9 (2006), 323-336.
A non-commutative BGG correspondence, Pacific J. Math. 218 (2005), 357-377.
Ext vanishing and infinite Auslander-Buchsbaum, Proc. Amer. Math. Soc. 133 (2005), 1335-1341.
Auslander-Reiten sequences on schemes, Ark. Mat. 44 (2006), 97-103.
Finite flat and projective dimension, Comm. Algebra 33 (2005), 2275-2279.
The homotopy category of complexes of projective modules, Adv. Math. 193 (2005), 223-232.
Existence of Gorenstein projective resolutions and Tate cohomology, J. Eur. Math. Soc. (JEMS) 9 (2007), 59-76.
With Henrik Holm: Cohen-Macaulay homological dimensions, Rend. Sem. Mat. Univ. Padova 117 (2007), 87-112.
With Henrik Holm: Semidualizing modules and related Gorenstein homological dimensions, J. Pure Appl. Algebra 205 (2006), 423-445.
Symmetry theorems for Ext vanishing, J. Algebra 301 (2006) 224-239.
Finite Cohen-Macaulay type and smooth non-commutative schemes, Canad. J. Math. 60 (2008), 379-390.
Recollement for Differential Graded Algebras, J. Algebra 299 (2006), 589-601.
A new recollement for schemes, Houston J. Math. 35 (2009), 1071-1077.
Amplitude inequalities for Differential Graded modules, Forum Math. 22 (2010), 941-948.
With Henrik Holm: Compactly generated homotopy categories, Homology, Homotopy Appl. 9 (2007), 257-274.
With Henrik Holm: Covers, precovers, and purity, Illinois J. Math. 52 (2008), 691-703.
Auslander-Reiten triangles in subcategories, J. K-theory 3 (2009), 583-601.
Quotients of cluster categories, Proc. Roy. Soc. Edinburgh Sect. A 140 (2010), 65-81.
Reflecting recollements, Osaka J. Math. 47 (2010), 209-213.
With Anders J. Frankild: Homological properties of cochain Differential Graded algebras, J. Algebra 320 (2008), 3311-3326.
Calabi-Yau categories and Poincaré duality spaces, pp. 399-431 in "Trends in representation theory of algebras and related topics" (edited by Andrzej Skowroński), European Mathematical Society Publishing House, Zürich, 2008.
With Thorsten Holm: On the relation between cluster and classical tilting, J. Pure Appl. Algebra 214 (2010), 1523-1533.
With Matthew Grime: Compactly generated relative stable categories, Algebr. Represent. Theory 14 (2011), 247-251.
With Henrik Holm: Rings without a Gorenstein analogue of the Govorov-Lazard Theorem, Q. J. Math. 62 (2011), 977-988.
With Thorsten Holm: On a cluster category of infinite Dynkin type, and the relation to triangulations of the infinity-gon, Math. Z. 270 (2012), 277-295.
With Henrik Holm: Cotorsion pairs induced by duality pairs, Journal of Commutative Algebra 1 (2009), 621-633.
With Kiriko Kato: Symmetric Auslander and Bass categories, Math. Proc. Cambridge Phil. Soc. 250 (2011), 227-240.
With Thorsten Holm: Triangulated categories: Definitions, properties and examples, pp. 1-51 in "Triangulated categories" (edited by Holm, Jørgensen, and Rouquier), London Math. Soc. Lecture Note Ser., Vol. 375, Cambridge University Press, Cambridge, 2010.
With Yann Palu: A Caldero-Chapoton map for infinite clusters, Trans. Amer. Math. Soc. 365 (2013), 1125-1147.
With Thorsten Holm and Martin Rubey: Ptolemy diagrams and torsion pairs in the cluster category of Dynkin type An, J. Algebraic Combin. 34 (2011), 507-523.
Duality for cochain DG algebras, Sci. China Ser. A 56 (2013), 79-89.
With Thorsten Holm and Dong Yang: Sparseness of t-structures and negative Calabi-Yau dimension in triangulated categories generated by a spherical object, Bull. London Math. Soc. 45 (2013), 120-130.
With David Pauksztello: The co-stability manifold of a triangulated category, Glasg. Math. J. 55 (2013), 161-175.
With Thorsten Holm: Realising higher cluster categories of Dynkin type as stable module categories, Q. J. Math. 64 (2013), 409-435.
With Kiriko Kato: Triangulated subcategories of extensions, stable t-structures, and triangles of recollements, J. Pure Appl. Algebra 219 (2015), 5500-5510.
With Thorsten Holm: Cluster tilting vs. weak cluster tilting in Dynkin type A infinity, Forum Math. 27 (2015), 1117-1137.
With Thorsten Holm and Martin Rubey: Torsion pairs in cluster tubes, J. Algebraic Combin. 39 (2014), 587-605.
With David Pauksztello: Classification of co-slicings and co-t-structures for the Kronecker algebra, J. Pure Appl. Algebra 219 (2015), 569-590.
With Thorsten Holm: SL2-tilings and triangulations of the strip, J. Combin. Theory Ser. A 120 (2013), 1817-1834.
With Thorsten Holm and Martin Rubey: Ptolemy diagrams and torsion pairs in the cluster categories of Dynkin type D, Adv. in Appl. Math. 51 (2013), 583-605.
With Christine Bessenrodt and Thorsten Holm: Generalized frieze pattern determinants and higher angulations of polygons, J. Combin. Theory Ser. A 123 (2014), 30-42.
With Thorsten Holm: Generalised friezes and a modified Caldero-Chapoton map depending on a rigid object, Nagoya Math. J. 218 (2015), 101-124.
With Osamu Iyama and Dong Yang: Intermediate co-t-structures, two-term silting objects, tau-tilting modules, and torsion classes, Algebra and Number Theory 8 (2014), 2413-2431.
With Thorsten Holm: Generalised friezes and a modified Caldero-Chapoton map depending on a rigid object, II, Bull. Sci. Math. 140 (2016), 112-131.
Torsion classes and t-structures in higher homological algebra, Internat. Math. Res. Notices 2016 (2016), 3880-3905.
With Christine Bessenrodt and Thorsten Holm: All SL2-tilings come from infinite triangulations, Adv. Math. 315 (2017), 194-245.
Co-t-structures: The First Decade, pp. 25-36 in "Surveys in Representation Theory of Algebras" (edited by Martsinkovsky, Igusa, and Todorov), Contemporary Mathematics, Vol. 716, Amer. Math. Soc., Providence, RI, 2018.
With Henrik Holm: Cotorsion pairs in categories of quiver representations, Kyoto J. Math. 59 (2019), 575-606.
With Martin Herschend and Laertis Vaso: Wide subcategories of d-cluster tilting subcategories, Trans. Amer. Math. Soc. 373 (2020), 2281-2309.
With Thorsten Holm: A p-angulated generalisation of Conway and Coxeter's theorem on frieze patterns, Internat. Math. Res. Notices 2020 (2020), 71-90.
With Milen Yakimov: c-vectors of 2-Calabi-Yau categories and Borel subalgebras of 𝖘𝖑∞, Selecta Math. (N.S.) 26 (2020), Art. 1.
With Sira Gratz and Thorsten Holm: Cluster tilting subcategories and torsion pairs in Igusa-Todorov cluster categories of Dynkin type A∞, Math. Z. 292 (2019), 33-56.
With Karin M. Jacobsen: d-abelian quotients of (d+2)-angulated categories, J. Algebra 521 (2019), 114-136.
Tropical friezes and the index in higher homological algebra, Math. Proc. Cambridge Philos. Soc. 171 (2021), 23--49.
With Karin M. Jacobsen: Maximal τd-rigid pairs, J. Algebra 546 (2020), 119-134.
With Henrik Holm: Model categories of quiver representations, Adv. Math. 357 (2019), 106826.
With Michael Cuntz and Thorsten Holm: Frieze patterns with coefficients, Forum Math. Sigma 8 (2020), e17.
With Milen Yakimov: Green groupoids of 2-Calabi-Yau categories, derived Picard actions, and hyperplane arrangements, Trans. Amer. Math. Soc. 375 (2022), 7981-8031.
With Martin Herschend: Classification of higher wide subcategories for higher Auslander algebras of type A, J. Pure Appl. Algebra 225 (2021), 106583.
With Ilke Canakci: Friezes, weak friezes, and T-paths, Adv. in Appl. Math. 131 (2021), 102253.
Abelian subcategories of triangulated categories induced by simple minded systems, Math. Z. 301 (2022), 565-592.
With J. Asadollahi, S. Schroll, and H. Treffinger, On higher torsion classes, Nagoya Math. J. 248 (2022), 823-848.
With H. Holm, The Q-shaped derived category of a ring, J. London Math. Soc. (2) 106 (2022), 3263--3316.
With H. Holm, The Q-shaped derived category of a ring -- compact and perfect objects, Trans. Amer. Math. Soc. 377 (2024), 3095-3128.
With T. Holm, Weak friezes and frieze pattern determinants, Proc. Amer. Math. Soc. 152 (2024), 1479--1491.
Preprints
The following manuscripts are not yet published.
With A. Shah, Grothendieck groups of d-exangulated categories and a modified Caldero-Chapoton map, to appear in J. Pure Appl. Algebra.
Proper abelian subcategories of triangulated categories and their tilting theory, preprint (2021).
With A. Shah, The index with respect to a rigid subcategory of a triangulated category, to appear in Internat. Math. Res. Notices.
With H. Holm, A brief introduction to the Q-shaped derived category, to appear in the Proceedings of the Abel Symposium 2022.
With F. Fedele and A. Shah, The index with respect to a contravariantly finite subcategory, preprint (2024).
With M. Cuntz and T. Holm, Noncommutative frieze patterns with coefficients, preprint (2024).
With H. Holm, Minimal semiinjective resolutions in the Q-shaped derived category, preprint (2024).
With F. Fedele and A. Shah, The index in d-exact categories, preprint (2024).
Book edited
"Triangulated categories" (edited by Holm, Jørgensen, and Rouquier), London Math. Soc. Lecture Note Ser., vol. 375, Cambridge University Press, Cambridge, 2010
Unpublished notes
Non-commutative projective geometry, expository notes (1996).
Synthetic commutative algebra, the summary of my Ph.D. thesis (1997).
Homological algebra, the slides from a lecture series given at Osaka Prefecture University (2008).
Higher dimensional homological algebra, notes from the LMS-CMI Research School "New trends in representation theory" at the University of Leicester (2017).