Vita, Publications, and Preprints

The documents are in the pdf format; the final versions are available on the math arXiv. Scroll down for books, some lecture notes etc.

Vita
(updated: November 2012)

Module categories for group algebras over commutative rings (with D. Benson and H. Krause)
preprint 2012.

DG algebras with exterior homology (with W. G. Dwyer and J. P. C. Greenlees)
preprint 2012.

Thick subcategories of the bounded derived category of a finite group (with J. F. Carlson)
preprint 2012.

Bass numbers over local rings via stable cohomology (with L. L. Avramov)
J. Comm. Alg. (to appear)

The Bousefield lattice of a triangulated category and stratification (with H. Krause)

Math. Z. (to appear)

Colocalizing subcategories and cosupport (with D. Benson and H. Krause)
J. Reine. Angew. Math. (to appear)

Detecting flatness over smooth bases (with L. L. Avramov)
J. Alg. Geom. (to appear)

Homological invariants of modules over contracting endomorphisms (with L. L. Avramov, M. Hochster, and Y. Yao)

Math. Ann. 353 (2012) 275–291.


Localising subcategories for cochains on the classifying space of a finite group (with D. Benson and H. Krause)

Comptes Rendus Acad. Sci. Ser I 349 (2011) 953--956.

Module categories for finite group algebras (with D. Benson and H. Krause)
Proceedings of ICRA XIV (Tokyo, 2010)  Eur. Math. Soc. Series of Congress Reports, 2011, 55--84.

Rigidity and reflexivity for complexes, II: Schemes (with L. L. Avramov and J. Lipman)
Algebra Number Theory 5 (2011) 379--429.
 

Stratifying triangulated categories (with D. Benson and H. Krause)
J. Topology 4 (2011) 641--666; published version.

Gross-Hopkins duality and the Gorenstein condition (with W. G. Dwyer and J. P. C. Greenlees)
J. K-theory 8 (2011) 107--133.

Stratifying modular representations of finite groups (with D. Benson and H. Krause)

Ann. of Math.  174 (2011) 1643--1684.


Short Koszul modules (with L. L. Avramov and L. M. Sega)

J. Comm. Alg. 2 (2010) 249--280.


Free resolutions over commutative Koszul algebras (with L. L. Avramov and A. Conca) 

Math. Res. Letters 17 (2010) 197--210.


Support and injective resolutions over commutative rings (with X.-W. Chen)

Homology, Homotopy, Appl. 12 (2010) 39--44.


Rigidity and reflexivity for complexes, I: Commutative rings (with L. L. Avramov and J. Lipman)

Algebra Number Theory  4 (2010) 47--86.


Reduction of derived Hochschild functors over commutative algebras and schemes 
(with L. L. Avramov, J. Lipman, and S. Nayak)
Adv. Math. 30 (2010) 735--772.


Cohomology over complete intersections via exterior algebras (with L. L. Avramov)

Triangulated categories (Leeds, 2006), London Math. Soc. Lecture Note Ser. 375, Cambridge Univ. Press, Cambridge, 2010, 52--75.


Dimensions of triangulated categories via Koszul objects (with P. Bergh, H. Krause, and S. Oppermann)

Math. Z. 265 (2010) 849--864.

Homology of perfect complexes (with L. L. Avramov, R-O. Buchweitz, and C. Miller)
Adv. Math. 223 (2010) 1731--1781
; Corrigendum Adv. Math. 225 (2010) 3576--3578

Homological dimensions and regular rings (with A. Iacob) 

J. Algebra 322 (2009) 3451--3458.


On the existence of star products on quotient spaces of linear Hamiltonian torus actions (with M. Pflaum and H.-C. Herbig)

Lett. Math. Phys. 89 (2009) 101--113


Linearity defects of modules over commutative rings (with T. Roemer)

J. Algebra 322 (2009) 3212--3237.


Free resolutions over short local rings (with L. L. Avramov and L. M. Sega)

J. London Math. Soc. 78 (2008) 459--476


Gorenstein algebras and Hochschild cohomology (with L. L. Avramov)

Michigan Math. Jour. 57 (2008) 17--35


Noncoherent subsets of Spec A (Appendix to: Thick subcategories of modules over commutative rings, by H. Krause)

Math. Ann. 340 (2008) 733--747


Local cohomology and support for triangulated categories (with D. Benson and H. Krause)

Ann. Sci.  École Norm. Sup. (4) 41 (2008), 575--621


Constructing modules with prescribed cohomological support (with L. L. Avramov)

Ill. Jour. Math. 51 (2007) 1--20


André-Quillen homology of commutative algebras

in: Interactions between homotopy theory and algebra (Chicago 2004), Contemp. Math. 436, Amer. Math. Soc., Providence, RI 2007


Class and rank of differential modules (with L. L. Avramov and R-O. Buchweitz)

Invent. Math. 169 (2007) 1--35


Gorenstein dimension of modules over homomorphisms (with L. Christensen) 

J. Pure Appl. Algebra 208 (2007) 177--188


Hilbert-Samuel functions of modules over Cohen-Macaulay rings (with T. Puthenpurakal) 

Proc. Amer. Math. Soc. 135 (2007) 637--648


A criterion for regularity of local rings (with T. Bridgeland)

Comptes Rendus Acad. Sci. Ser I, 342 (2006) 723--726


Acyclicity versus total acyclicity for complexes over commutative rings (with H. Krause)

Documenta Math. 11 (2006) 207--240 Electronic publication at Documenta Math.


Finiteness in derived categories of local rings (with W. Dwyer and J. P. C. Greenlees) 

Comment. Math. Helv. 81 (2006) 383--432


Homology over local homomorphisms (with L. Avramov and C. Miller) 

American Jour. Math. 128 (2006) 23--90


Duality in algebra and topology (with W. Dwyer and J. P. C. Greenlees)

Adv. Math. 200 (2006) 357--402.


Gaps in Hochschild cohomology imply smoothness for commutative algebras (with L. Avramov) 

Math. Res. Letters 12 (2005) 789--804


Koszul modules (with J. Herzog)

J. Pure Appl. Algebra 201 (2005) 154--188.


Modules and cohomology over group algebras. One commutative algebraist's perspective.
 
in: Trends in commutative algebra (Berkeley, September 2002), 
MSRI Publ. Vol. 51, Cambridge Univ. Press, Cambridge, 2004; 51--86

G-dimension over local homomorphisms. Applications to the Frobenius endomorphism(with S. Sather-Wagstaff)

Ill. Jour. Math. 48 (2004) 241--272. Electronic publication at IJM


Dualizing DG modules and Gorenstein DG algebras ( with A. Frankild and P. Jørgensen)

J. London Math. Soc. 68 (2003) 288--306.


Depth and amplitude for unbounded complexes   (with H.-B. Foxby)

in: Commutative Algebra. Its interaction with Algebraic Geometry (Grenoble-Lyon 2001), Contemp. Math. 331,  A.M.S., R.I., 2003; 119--137.


Andre-Quillen homology of algebra retracts     (with L. Avramov)

Ann. Sci.  École Norm. Sup. (4) 36 (2003) 431--462.


Homological criteria for regular homomorphisms and for locally complete intersection homomorphism (with L. Avramov)

in: Algebra, Arithmetic, and Geometry (Mumbai 2000) T.I.F.R. Studies in Math. 16 vol. I, Narosa, New Delhi, 2002; 97--122.


Acyclicity of Tate constructions

J.Pure Appl. Algebra 163 (2001), no. 3, 289--300.


On a depth formula for modules over local rings (with S. Choi)

Comm. Algebra, 29 (2001) 3135--3143.


Finite generation of hochschild homology algebras (with L. Avramov)

Invent. Math., 140 (2000) 143--170.


Free summands of conormal modules and central elements in homotopy lie algebras of local rings

Proc. Amer. Math. Soc., 129 (2001) 1563--1572.


Maximal minimal resolutions (with K. Pardue)

J. Reine. Angew. Math., 512 (1999) 27--48.


Depth for complexes, and intersection theorems

Math. Z., 230 (1999) 545--567.


Free resolutions and change of rings

J. Algebra, 190 (1997) 195--213.


Shifts in resolutions of multigraded modules

Math. Proc. Camb. Phil. Soc., 121 (1997) 437--441.



Books

Representations of finite groups: Local cohomology and support (with D. Benson and H. Krause)
Oberwolfach Seminar 43, Birkahaueser,  2011.

Twenty-four hours of local cohomology (with G. Leuschke, A. Leykin, C. Miller, E. Miller, A. Singh, and U. Walther) 
AMS Graduate Studies in Mathematics, Volume 87, 2007.


Lectures from some conferences

Commutative algebra and representations of finite groups,
INdAM day 2012, Genoa, Italy, 7th June 2012.

Flatness and torsion in tensor powers of modules over local rings,
7th Japan-Vietnam Joint Seminar on Commutative Algebra, Quy Nhon, Vietnam, 12--16 December 2011.

The Bousfield lattice of the stable module category of a finite group,
Workshop ``Representation Theory of Quivers and Finite Dimensional Algebras'', appears in Oberwolfach Report No. ??/2011.

Stratifying derived categories associated to finite groups and to commutative rings,
Workshop ``Algebraic triangulated categories and related topics'', Research Institute for Mathematical Sciences, Kyoto University, Japan, July 2009.

Stratifying the derived category of a complete intersection,
Workshop ``Kommutative Algebra'', appears in Oberwolfach Report No. 22/2009.

Levels in triangulated categories
Workshop on Triangulated Categories, University of Leeds, U.K., August 2006. Satellite of the ICM 2006.

Thick subcategories of perfect complexes over a commutative ring,
Mini-Workshop ``Thick subcategories - Classifications and applications'', appears in  Oberwolfach Report No. 8/2006.

Other items

Translation of "Local cohomology and finite projective dimension", by C. Peskine and L. Szpiro.