Prof. Dr. Henning Krause
Faculty of Mathematics
PO Box 100 131
Tel: +49 521 106-5020 (office)
Tel: +49 521 106-5021 (secretary)
Tel: +49 5251 2078378 (home)
Fax: +49 521 106-6482
Office hours: Monday 16:00 - 17:00 or by appointment (via email).
I am professor of mathematics at Bielefeld University since 2010 and
member of the Bielefeld
Representation Theory Group (BIREP). Previous appointments were at Paderborn (2003 - 2010) and Leeds (2002 - 2003). For more details
see my CV.
I am involved in two major research projects:
I am an editorial board member for these journals:
Publications since 2000
- Smashing subcategories and the telescope conjecture—an
algebraic approach, Invent. Math. 139 (2000), 99–133.
- (With G. Zwara) Stable equivalence and generic modules,
Bull. London Math. Soc. 32 (2000), 615–618.
- Finite versus infinite dimensional representations—a new
definition of tameness, in: Infinite length modules (Bielefeld,
1998), 393–403, Birkhäuser, Basel, 2000.
- (With D. J. Benson) Generic idempotent modules for a finite
group, Algebras and Representation Theory 3 (2000), 337–346.
- Auslander–Reiten theory via Brown representability, K-theory 20
- (With U. Reichenbach) Endofiniteness in stable homotopy theory,
Trans. Amer. Math. Soc. 353 (2001), 157–173.
- Brown representability and flat covers, J. Pure Appl. Algebra
157 (2001), 81–86.
- On Neeman's well generated triangulated categories, Documenta
Math. 6 (2001), 119–125.
- (With D. J. Benson) Pure injectives and the spectrum of the
cohomology ring of a finite group, J. reine angew. Math. 542 (2002),
- (With A. B. Buan and Ø. Solberg) On the lattice of cotilting
modules, AMA Algebra Montp. Announc. 1 (2002), 6 pp.
- A Brown representability theorem via coherent functors,
Topology 41 (2002), 853–861.
- Coherent functors in stable homotopy theory, Fundamenta Math.
173 (2002), 33–56.
- A duality between complexes of right and left modules, in:
Representations of algebra. Vol. I, 87–97, Beijing
Norm. Univ. Press, Beijing, 2002.
- (With C. Geiss) On the notion of derived tameness, J. Algebra
and Applications 1 (2002), 133–157.
- A short proof for Auslander's defect formula, Linear Algebra
Appl. 365 (2003), 267–270.
- (With Ø. Solberg) Filtering modules with finite projective
dimension, Forum Math. 15 (2003), 377–393.
- (With A. Beligiannis) Realizing maps between modules over Tate
cohomology rings, Beiträge Algebra Geom. 44 (2003), 451–466.
- (With A. B. Buan) Cotilting modules over tame hereditary
algebras, Pacific J. Math. 211 (2003), 41–59.
- Uniqueness of uniform decompositions in abelian categories,
J. Pure Appl. Algebra 183 (2003), 125–128.
- (With Ø. Solberg) Applications of cotorsion pairs, J. London
Math. Soc. 68 (2003), 631–650.
- Coherent functors and covariantly finite subcategories, Algebras
and Representation Theory 6 (2003), 475–499.
- (With A. B. Buan) Tilting and cotilting for quivers of type An,
J. Pure Appl. Algebra 190 (2004), 1–21.
- (With D. J. Benson and S. Schwede) Realizibility of modules over
Tate cohomology, Trans. Amer. Math. Soc. 356 (2004), 3621–3668.
- Auslander–Reiten triangles and a theorem of Zimmermann,
Bull. London Math. Soc. 37 (2005), 361–372.
- The stable derived category of a noetherian scheme,
Compos. Math. 141 (2005), 1128–1162.
- (With D. J. Benson and S. Schwede) Introduction to realizability
of modules over Tate cohomology, in: Representations of algebras
and related topics, 81–97, Amer. Math. Soc., Providence, RI,
- Epimorphisms of additive categories up to direct factors,
J. Pure Appl. Algebra 203 (2005), 113–118.
- Cohomological quotients and smashing localizations,
Amer. J. Math. 127 (2005), 1191–1246.
- (With S. B. Iyengar) Acyclicity versus total acyclicity for
complexes over noetherian rings, Documenta Math. 11 (2006),
- (With D. Kussin) Rouquier's theorem on representation dimension,
in: Trends in representation theory of algebras and related topics,
95–103, Contemp. Math. 406, Amer. Math. Soc., Providence, RI,
- (With J. Le) The Auslander–Reiten formula for complexes of
modules, Adv. Math. 207 (2006), 133–148.
- Derived categories, resolutions, and Brown representability, in:
Interactions between homotopy theory and algebra, 101–139,
Contemp. Math. 436, Amer. Math. Soc., Providence, RI, 2007.
- (With A. B. Buan and Ø. Solberg) Support varieties: an ideal
approach, Homology, Homotopy Appl. 9 (2007), 45–74.
- An axiomatic characterization of the Gabriel–Roiter measure,
Bull. London Math. Soc. 39 (2007), 550–558.
- (With D. J. Benson) Complexes of injective kG-modules, Algebra
Number Theory 2 (2008), 1–30.
- (With an appendix by S. B. Iyengar) Thick subcategories of
modules over commutative rings, Math. Annalen 340 (2008),
- (With D. Benson and S. B. Iyengar) Local cohomology and support
for triangulated categories, Ann. Sci. Ecole Norm. Sup. (4) 41 (2008),
- (With A. Beligiannis) Thick subcategories and virtually
Gorenstein algebras, Illinois J. Math. 52 (2009), 551–562.
- (With P. A. Bergh, S. B. Iyengar and S. Oppermann) Dimensions of
triangulated categories via Koszul objects, Math. Z. 265 (2010),
- Localization theory for triangulated categories, in: Triangulated
categories, 161–235, London Math. Soc. Lecture Note Ser. 375,
Cambridge Univ. Press, Cambridge, 2010.
- (With J. Stovicek) The telescope conjecture for hereditary rings
via Ext-orthogonal pairs, Adv. Math. 225 (2010), 2341–2364.
- (With Y. Ye) On the centre of a triangulated category,
Proc. Edinburgh Math. Soc. 54 (2011), 443–466.
- (With X.-W. Chen) Expansions of abelian categories, J. Pure
Appl. Algebra 215 (2011), 2873–2883.
- (With D. J. Benson and S. B. Iyengar) Stratifying triangulated
categories, J. Topology 4 (2011), 641–666.
- (With D. J. Benson and S. B. Iyengar) Module categories for finite
group algebras, in: Representations of Algebras and Related Topics,
55-83, European Math. Soc., 2011.
- (With D. J. Benson and S. B. Iyengar) Localising subcategories for
cochains on the classifying space of a finite group,
C. R. Math. Acad. Sci. Paris 349 (2011), 953-956.
- (With D. J. Benson and S. B. Iyengar) Stratifying modular
representations of finite groups, Ann. of Math. 174 (2011),
- Approximations and adjoints in homotopy categories, Math. Annalen
353 (2012), 765-781.
- Report on locally finite triangulated categories, J. K-Theory 9
- (With D. J. Benson and S. B. Iyengar) Colocalizing subcategories
and cosupport, J. Reine Angew. Math. 673 (2012), 161-207.
- (With Mike Prest) The Gabriel-Roiter filtration of the Ziegler
spectrum, Quart. J. Math. 64 (2013), 891-901.
- (With S. B. Iyengar) The Bousfield lattice of a triangulated
category and stratification, Math. Z. 273 (2013), 1215-1241.
- (With D. J. Benson, S. B. Iyengar, and appendix by G. Stevenson)
Module categories for group algebras over commutative rings,
J. K-Theory 11 (2013), 297-329.
- Koszul, Ringel, and Serre duality for strict polynomial functors,
Compos. Math. 149 (2013), 996-1018.
- Abelian length categories of strongly unbounded type,
Int. Math. Res. Not. (2013), doi:10.1093/imrn/rnt184.
- (With Greg Stevenson) A note on thick subcategories of stable
derived categories, Nagoya Math. J. (2013),
- Morphisms determined by objects in triangulated categories, in:
Algebras, Quivers and Representations, The Abel Symposium 2011,
195-207, Abel Symposia 8, Springer, 2013.
- (With C. M. Ringel) Infinite
length modules, Proceedings of the Euroconference 'Infinite length
modules' 1998 in Bielefeld, Trends in
Mathematics, Birkhäuser Verlag, 2000, 440 pp.
spectrum of a module category, Mem. Amer. Math. Soc. 149 (2001),
no. 707, x+125 pp.
- (With L. Angeleri Hügel and D. Happel) Handbook Tilting Theory,
London Math. Soc. Lecture Note Ser. 332, Cambridge Univ. Press,
Cambridge, 2007, 480 pp.
- (With D. J. Benson and S. B. Iyengar) Representations
of finite groups: Local cohomology and support, Oberwolfach
Seminars 43, Birkhäuser Verlag, 2012, 111 pp.
- (With D. J. Benson and A. Skowronski) Advances
in Representation Theory of Algebras, EMS Publishing House, 2013, 378 pp.
- Cohomological length functions, arXiv:1209.0540.
- (With D. J. Benson and S. B. Iyengar) A local-global principle
for small triangulated categories, to appear in
Math. Proc. Camb. Phil. Soc., arXiv:1305.1668.
- (With A. Hubery) A categorification of non-crossing partitions, arXiv:1310.1907.
- Polynomial representations of GL(n) and Schur-Weyl duality, arXiv:1311.0820.
- (With G. Bobiński) The Krull-Gabriel dimension of discrete
derived categories, to appear in Bull. Sci. Math., arXiv:1402.1596.
- Morphisms determined by objects and flat covers, arXiv:1403.6039.
- The highest weight structure for strict polynomial functors, arXiv:1405.1691.
- Deriving Auslander's formula, arXiv:1409.7051.
Some notes and presentations
- Krull-Schmidt categories
and projective covers (June 2008, revised October 2014)
- Representations of quivers via reflection functors, arXiv:0804.1428.
- (With X.-W. Chen) Introduction to coherent sheaves on weighted
projective lines, arXiv:0911.4473.
- Notes on the Gabriel-Roiter measure, arXiv:1107.2631.
- Cosupport and colocalizing subcategories of modules
and complexes (Beijing, May 2010)
representations through local cohomology and support (Tokyo,
- Stratifying triangulated
categories: support and cosupport of complexes (Moscow,
- Functors and morphisms
determined by objects revisited (Shanghai, October 2011)
- Koszul, Ringel, and Serre
duality for strict polynomial functors (Woods Hole, Banff and Guanajuato, April/May
- Notes on local cohomology
and support (Summer 2013)
- Michael Butler - From
abelian groups to strings and bands (Sherbrooke, October
- Relative homological
algebra in triangulated categories (Aberdeen, November
determined by objects and flat covers (Spineto, June
- Stratifying triangulated
categories: support and cosupport of complexes (Nantes,
- Stratification of
triangulated categories (Notes by Pieter Belmans from a summer
school at Nantes, June 2014)
Recent and forthcoming meetings
"Representation Theory of Quivers and Finite Dimensional
Algebras" (Oberwolfach, February 20 - 26, 2011)
Schwerpunkttagung 2011 (Münster, March 1 - 4, 2011)
"Matrix Factorizations" (Bielefeld, May 6 - 8, 2011)
"Representation Theory: Cohomology and Support" (Morningside
Center of Mathematics, Beijing, September 26 - 30, 2011)
Groups 2012 – A conference in honour of the 75th
birthday of Bernd Fischer (Bielefeld, March 12 - 16, 2012)
- Summer School
and Workshop "Cohomology and Support in Representation Theory" (Seattle, July 27 - August 5, 2012)
and International Conference "Representations of Algebras (ICRA
2012)" (Bielefeld, August 8 - 17, 2012)
in memoriam of Dieter Happel (Chemnitz, May 4 - 6, 2013)
"Matrix Factorizations in Algebra, Geometry, and Physics
" (Oberwolfach, September 1 - 7, 2013)
"Polynomial functors and Schur algebras" (Bielefeld,
November 7 - 9, 2013)
"Representation Theory of Quivers and Finite Dimensional
Algebras" (Oberwolfach, February 16 - 22, 2014)
"Colloquium in honour of the 75th birthday of Helmut Lenzing" (Bielefeld,
May 15 - 16, 2014)
"Non-crossing partitions in representation theory" (Bielefeld,
June 12 - 14, 2014)
program "Interactions between Representation Theory, Algebraic
Topology and Commutative Algebra" (CRM Barcelona, Jan 7 - Jun 30,
"Cohomology of Finite Groups: Interactions and Applications"
(Oberwolfach, May 3 - 9, 2015)
Groups, Representations and Cohomology: Summer School and Conference
in honour of Dave Benson's 60th birthday (Isle of Skye, June 19 - 26, 2015)
About my family
- Next generation: A picture of my
two children Judith and Simon taking off
(from the ruins of St. Petri at Kloster Dalheim).
- Previous generations: The lecture of
on the occasion of his 60th Doktorjubiläum. Incidentally, his
was teaching the same subject at the same school, while his
was coming from a different direction; see a biographical
entry from "Allgemeine Deutsche Biographie", Zwanzigster
Band, Königl. Akademie der Wissenschaften, Leipzig, 1884.