Publications

 Valid HTML 5

Preprints

  • Lars Winther Christensen, Orin Gotchey, and Alexis Hardesty,
    Sampling algebra structures on minimal free resolutions of length 3.

    [ Preprint (2023), 20 pp. ]

Journal Articles

  1. Lars Winther Christensen and Luigi Ferraro, The Improved New Intersection Theorem revisited,
    Michigan Math. J., to appear (online Jan. 2024), 8 pp.   [ Preprint ]
  2. Lars Winther Christensen, Sergio Estrada, Li Liang, Peder Thompson, and Junpeng Wang,
    One-sided Gorenstein rings, Forum Math., to appear (online Jan. 2024), 23 pp.  [ Preprint ]
  3. Lars Winther Christensen, Luigi Ferraro, and Peder Thompson,
    Rigidity of Ext and Tor via flat–cotorsion theory, Proc. Edinb. Math. Soc. 66 (2023), 1142–1153.
    [ Preprint  MR4679218  Zbl 1532.13018 ]
  4. Lars Winther Christensen and Oana Veliche,
    Generic local rings on a spectrum between Golod and Gorenstein,
    Adv. Appl. Math. 151 (2023), paper no. 102580, 55 pp.   [ Preprint  MR4616997  Zbl 07737682 ]
  5. Lars Winther Christensen, Nanqing Ding, Sergio Estrada, Jiangsheng Hu, Huanhuan Li, and Peder Thompson,
    The singularity category of an exact category applied to characterize Gorenstein schemes,
    Quart. J. Math. 74 (2023), 1–27.   [ Preprint  MR4571621  Zbl 1515.14029 ]
  6. Lars Winther Christensen, Sergio Estrada, and Peder Thompson,
    Gorenstein weak global dimension is symmetric,
    Math. Nachr. 294 (2021), 2121–2128.   [ Preprint  MR4371287  Zbl 07747377 ]
  7. Lars Winther Christensen, Sergio Estrada, and Peder Thompson,
    The stable category of Gorenstein flat sheaves on a noetherian scheme,
    Proc. Amer. Math. Soc 149 (2021), 525–538.   [ Preprint  MR4198062  Zbl 1457.14036 ]
  8. Lars Winther Christensen, Sergio Estrada, Li Liang, Peder Thompson, Dejun Wu, and Yang Gang,
    A refinement of Gorenstein flat dimension the via the flat–cotorsion theory,
    J. Algebra 567 (2021), 346–370.   [ Preprint  MR4159258  Zbl 1478.16004 ]
  9. Lars Winther Christensen, Oana Veliche, and Jerzy Weyman,
    Minors of a skew symmetric matrix: a combinatorial approach,
    Electron. J. Linear Algebra, 36 (2020), 658–663.   [ Preprint  MR4165809  Zbl 1452.15002 ]
  10. Lars Winther Christensen, Oana Veliche, and Jerzy Weyman, Linkage classes of grade 3 perfect ideals,
    J. Pure Appl. Algebra 224 (2020), paper no. 106185, 29 pp.   [ Preprint  MR4048506  Zbl 1440.13056 ]
  11. Lars Winther Christensen, Oana Veliche, and Jerzy Weyman, Trimming a Gorenstein ideal,
    J. Commut. Algebra 11 (2019), 325–339.   [ Preprint  MR4038053  Zbl 1441.13059 ]
  12. Lars Winther Christensen and Peder Thompson, Pure-minimal chain complexes,
    Rend. Semin. Mat. Univ. Padova 142 (2019), 41–67.   [ Preprint  MR4032803  Zbl 1454.16001 ]
  13. Lars Winther Christensen, Oana Veliche, and Jerzy Weyman,
    Free resolutions of Dynkin format and the licci property of grade 3 perfect ideals,
    Math. Scand. 125 (2019), 163–178.   [ Preprint  MR4031044  Zbl 1451.13044 ]
  14. Lars Winther Christensen and Dejun Wu,
    A Bass equality for Gorenstein injective dimension of modules finite over homomorphisms,
    Arch. Math. (Basel) 113 (2019), 459–467.   [ Preprint  MR4016630  Zbl 1430.13019 ]
  15. Lars Winther Christensen, Srikanth B. Iyengar, and Thomas Marley,
    Rigidity of Ext and Tor with coefficients in residue fields of a commutative noetherian ring,
    Proc. Edinb. Math. Soc. 62 (2019), 305–321.   [ Preprint  MR3935802  Zbl 1412.13020 ]
  16. Lars Winther Christensen and Oana Veliche,
    The Golod property of powers of the maximal ideal of a local ring,
    Arch. Math. (Basel) 110 (2018), 549–562.   [ Preprint  MR3803744  Zbl 1393.13043 ]
  17. Lars Winther Christensen and Kirko Kato, Totally acyclic complexes and locally Gorenstein rings,
    J. Algebra Appl. 17 (2018), 1850039, 6 pp.   [ Preprint  MR3760008  Zbl 1390.13042 ]
  18. Olgur Celikbas, Lars Winther Christensen, Li Liang, and Greg Piepmeyer,
    Complete homology over associative rings, Israel J. Math. 221 (2017), 1–24.  
    [ Preprint  MR3705846  Zbl 1428.16007 ]
  19. Olgur Celikbas, Lars Winther Christensen, Li Liang, and Greg Piepmeyer,
    Stable homology over associative rings, Trans. Amer. Math. Soc. 369 (2017), 8061–8086.
    [ Preprint  MR3695854  Zbl 1397.16007 ]
  20. Lars Winther Christensen and Srikanth B. Iyengar, Tests for injectivity of modules over commutative rings, Collect. Math. 68 (2017), 243–250.   [ Preprint  MR3633060  Zbl 1372.13007 ]
  21. Lars Winther Christensen, Sergio Estrada, and Alina Iacob,
    A Zariski-local notion of F-total acyclicity for complexes of sheaves,
    Quaest. Math., 40 (2017), 197–214.   [ Preprint  MR3630500  Zbl 1423.18047 ]
  22. Lars Winther Christensen, Fatih Köksal, and Li Liang, Gorenstein dimensions of unbounded complexes
    and change of base (With an appendix by Driss Bennis)    , Sci. China Math. 60 (2017), 401–420.
    [ Preprint  MR3600932  Zbl 1381.13006 ]
  23. Lars Winther Christensen and Fatih Köksal, Injective modules under faithfully flat ring extensions,
    Proc. Amer. Math. Soc. 144 (2016), 1015–1020.   [ Preprint  MR3447655  Zbl 1361.13006 ]
  24. Jesse Burke, Lars Winther Christensen, and Ryo Takahashi, Building modules from the singular locus,
    Math. Scand. 116 (2015), 23–33.   [ Preprint  MR32322605  Zbl 1310.13019 ]
  25. Lars Winther Christensen and David A. Jorgensen,
    Vanishing of Tate homology and depth formulas over local rings,
    J. Pure Appl. Algebra 219 (2015), 464–481.   [ Preprint  MR3279366  Zbl 1311.13016 ]
  26. Lars Winther Christensen and Henrik Holm, The direct limit closure of perfect complexes,
    J. Pure Appl. Algebra 219 (2015), 449–463.   [ Preprint  MR3279365  Zbl 1357.16015 ]
  27. Lars Winther Christensen and Oana Veliche, Local rings of embedding codepth 3:
    A classification algorithm    , J. Softw. Algebra Geom. 6 (2014), 1–8.   [ Preprint  MR3338667  Zbl 1401.13081 ]

    [ Accompanying Macaulay2 package CodepthThree ]

  28. Lars Winther Christensen and Oana Veliche, Local rings of embedding codepth 3. Examples,
    Algebr. Represent. Theory 17 (2014), 121–135.   [ Preprint  MR3160716  Zbl 1295.13019 ]
  29. Lars Winther Christensen and David A. Jorgensen, Tate (co)homology via pinched complexes,
    Trans. Amer. Math. Soc. 366 (2014), 667–689.   [ Preprint  MR3130313  Zbl 1326.18008 ]
  30. Lars Winther Christensen and Henrik Holm, Vanishing of cohomology over Cohen–Macaulay rings,
    Manuscripta Math. 139 (2012), 535–544.   [ Preprint  MR2974289  Zbl 1255.13009 ]
  31. Lars Winther Christensen, David A. Jorgensen, Hamidreza Rahmati, Janet Striuli, and Roger Wiegand,
    Brauer–Thrall for totally reflexive modules, J. Algebra 350 (2012), 340–373.
    [ Preprint  MR2859892  Zbl 1274.13026 ]
  32. Lars Winther Christensen and Henrik Holm,
    Algebras that satisfy Auslander's condition on vanishing of cohomology,
    Math. Z. 265 (2010), 21–40.   [ Preprint  MR2606948  Zbl 1252.16008 ]
  33. Lars Winther Christensen and Sean Sather-Wagstaff,
    Transfer of Gorenstein dimensions along ring homomorphisms,
    J. Pure Appl. Algebra 214 (2010), 982–989.   [ Preprint  MR2580673  Zbl 1186.13010 ]
  34. Lars Winther Christensen, Janet Striuli, and Oana Veliche,
    Growth in the minimal injective resolution of a local ring,
    J. Lond. Math. Soc. 81 (2010), 24–44    .   [ Preprint  MR2580452  Zbl 1190.13018 ]
  35. Lars Winther Christensen and Sean Sather-Wagstaff, Descent via Koszul extensions,
    J. Algebra 322 (2009), 3026–3046.   [ Preprint  MR2567408  Zbl 1186.13024 ]
  36. Lars Winther Christensen and Henrik Holm, Ascent properties of Auslander categories,
    Canad. J. Math. 61 (2009), 76–108.   [ Preprint  MR2488450  Zbl 1173.13016 ]
  37. Lars Winther Christensen and Sean Sather-Wagstaff,
    A Cohen–Macaulay algebra has only finitely many semidualizing modules,
    Math. Proc. Cambridge Philos. Soc. 145 (2008), 601–603.   [ Preprint  MR2464778  Zbl 1153.13020 ]
  38. Lars Winther Christensen, Greg Piepmeyer, Janet Striuli, and Ryo Takahashi,
    Finite Gorenstein representation type implies simple singularity,
    Adv. Math. 218 (2008), 1012–1026.   [ Preprint  MR2419377  Zbl 1148.14004 ]
  39. Lars Winther Christensen and Oana Veliche, A test complex for Gorensteinness,
    Proc. Amer. Math. Soc. 136 (2008), 479–487.   [ Preprint  MR2358487  Zbl 1131.13021 ]
  40. Lars Winther Christensen and Oana Veliche, Acyclicity over local rings with radical cube zero,
    Illinois J. Math. 54 (2007), 1439–1454.   [ Preprint  MR2417436  Zbl 1148.13004 ]
  41. Lars Winther Christensen and Srikanth Iyengar, Gorenstein dimension of modules over homomorphisms,
    J. Pure Appl. Algebra 208 (2007), 177–188.   [ Preprint  MR2269838  Zbl 1105.13014 ]
  42. Lars Winther Christensen, Anders Frankild, and Henrik Holm,
    On Gorenstein projective, injective and flat dimensions—A functorial description with applications,
    J. Algebra 302 (2006), 231–279.   [ Preprint  MR2236602  Zbl 1104.13008 ]
  43. Lars Winther Christensen, Sequences for complexes II,
    Math. Scand. 91 (2002), 161–174.   [ Preprint  MR1931568  Zbl 1021.13015 ]
  44. Lars Winther Christensen, Hans-Bjørn Foxby, and Anders Frankild,
    Restricted homological dimensions and Cohen–Macaulayness,
    J. Algebra 251 (2002), 479–502.   [ Preprint  MR1900297  Zbl 1073.13501 ]
  45. Lars Winther Christensen, Sequences for complexes,
    Math. Scand. 89 (2001), 161–180.   [ Preprint  MR1868172  Zbl 1021.13014 ]
  46. Lars Winther Christensen, Semi-dualizing complexes and their Auslander categories,
    Trans. Amer. Math. Soc. 353 (2001), 1839–1883.   [ Preprint  MR1813596  Zbl 0969.13006 ]
 

Book Chapters

Lars Winther Christensen, Sergio Estrada, and Peder Thompson, Five theorems on Gorenstein global dimensions. In: A. Leroy and S. K. Jain (eds), Algebra and Coding Theory, 67–78, Contemp. Math. vol. 785.
Amer. Math.Soc., Providence RI, 2023.   [ Preprint   MR4586431  Zbl 07696850 ]
Lars Winther Christensen, Oana Veliche, and Jerzy Weyman, Three takes on almost complete intersection ideals of grade 3. In: I. Peeva (ed), Commutative Algebra: Expository Papers Dedicated to David Eisenbud
on the Occasion of his 75th Birthday, 219–281. Springer Nature, Cham, 2022.
[ Preprint  Errata  MR4394410  Zbl 1498.13019 ]
Lars Winther Christensen and Srikanth B. Iyengar, Dimension of finite free complexes over commutative noetherian rings. In: N. Baeth, T. Freitas, G. Leuschke, and V. H. J. Pérez (eds), Commutative Algebra: 150
years with Roger and Sylvia Wiegand, 11–17, Contemp. Math. vol. 773. Amer. Math. Soc., Providence RI, 2021.   [ Preprint  MR4321387  Zbl 1489.13022 ]
Lars Winther Christensen, Sergio Estrada, and Peder Thompson, Homotopy categories of totally acyclic complexes with applications to the flat–cotorsion theory. In: A. K. Srivastava, A. Leroy, I. Herzog,
and P. A. Guil Asensio (eds), Categorical, Homological and Combinatorial Methods in Algebra, 99–118,
Contemp. Math, vol. 751. Amer. Math. Soc., Providence RI, 2020.   [ Preprint  MR4132086  Zbl 1468.16009 ]
Lars Winther Christensen, Tate homology beyond Gorenstein rings.
In: D. Herbera, W. Pitsch, and S. Zarzuela (eds), Extended Abstracts Spring 2015, 47–51.
Trends in Mathematics, vol. 5. Birkhäuser, Cham, 2016.   [ Preprint ]
Lars Winther Christensen, Hans-Bjørn Foxby, and Henrik Holm, Beyond totally reflexive modules and back.
In: M. Fontana, S. E. Kabbaj, B. Olberding, and I. Swanson (eds), Commutative Algebra: Noetherian and non-Noetherian perspectives, 101–143. Springer-Verlag, New York NY, 2011. [ Preprint  MR2762509  Zbl 1225.13019 ]
 

Books

Lars Winther Christensen, Hans-Bjørn Foxby, and Henrik Holm,
Derived Category Methods in Commutative Algebra,
Springer Monographs in Mathematics, to appear.
Lars Winther Christensen, Gorenstein Dimensions,
Lecture Notes in Math. vol. 1747. Springer-Verlag, Berlin, 2000, xiii + 204 pp.
[ Errata  MR1799866  Zbl 0965.13010 ]

Software

Varia

 Home
Teaching
Publications
Curriculum Vitæ