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 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, The Q-shaped derived category of a ring -- compact and perfect objects, to appear in Trans. Amer. Math. Soc.
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).
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).