A. Langer's Papers

Research papers of Adrian Langer:

I give pdf files of some of the papers that are not the arXiv. Pdf files of other papers or preprints are available on request. Note that often the published version is quite different to the last version that I put on the arXiv (especially for older papers).

1. Fano schemes of linear spaces on hypersurfaces, Manuscripta Math. 93 (1997), 21-28.

2. On twistor curves of small degree, Quart. J. Math. Oxford 49 (1998), 43-58.

3. Fano 4-folds with scroll structure, Nagoya Math. J. 150 (1998), 135-176.

4. Adjoint linear systems on normal surfaces, J. Algebraic Geom. 8 (1999), 41-66.

5. A note on k-jet ampleness on surfaces, Contemp. Math. 241 (1999), 273-282.

6. Pluricanonical systems on surfaces with small K^2, International J. Math. 11 (2000), 379-392.

7. Chern classes of reflexive sheaves on normal surfaces, Math. Z. 235 (2000), 591-614.

8. Adjoint linear systems on normal surfaces II, J. Algebraic Geom. 9 (2000), 71-92.

9. Adjoint linear systems on normal log surfaces, Compositio Math. 129 (2001), 47-66.

10. The Bogomolov-Miyaoka-Yau inequality for log canonical surfaces, J. London Math. Soc. 64 (2001), 327-343.

11. A note on Bogomolov's instability and Higgs sheaves, in Algebraic Geometry: A Volume in Memory of Paolo Francia, (eds. M. Beltrametti et al.), Walter de Gruyter, 2002, 237-256.

12. Logarithmic orbifold Euler numbers with applications, Proc. London Math. Soc. (3) 86 (2003), 358-396.

13. Semistable sheaves in positive characteristic, Ann. of Math. 159 (2004), 251-276, AMS Review

14. Addendum to "Semistable sheaves in positive characteristic", Ann. of Math. 160 (2004), 1211-1213.

15. Moduli spaces of sheaves in mixed characteristic, Duke Math. J. 124 (2004), 571-586.

16. Semistable principal G-bundles in positive characteristic, Duke Math. J. 128 (2005), 511-540.

17. Moduli spaces and Castelnuovo--Mumford regularity of sheaves on surfaces, Amer. J. Math. 128 (2006), 373-417.

18. Lectures on torsion-free sheaves and their moduli, "Algebraic Cycles, Sheaves, Shtukas, and Moduli", (ed. Piotr Pragacz ), in Trends in Mathematics, 2008, Birkhauser, 69-103.

19. Moduli spaces for principal bundles in arbitrary characteristic, with T. Gomez, A. Schmitt and I. Sols, Adv. Math. 219 (2008), 1177-1245.

20. D-affinity and Frobenius morphism on quadrics, Int. Math. Res. Not. 2008, rnm145-26, published version

21. Erratum to "D-affinity and Frobenius morphism on quadrics", Int. Math. Res. Not. 2010, 1966-1972, published version

22. Moduli spaces of sheaves and principal G-bundles, in Algebraic Geometry: Seattle 2005, eds. D. Abramovich et al., Proc. Symp. Pure Math. 80 (2009), 273-308, a pdf file

23. Moduli spaces for principal bundles in large characteristic, with T. Gomez, A. Schmitt and I. Sols, in Teichmuller Theory and Moduli Problems, RMS Lecture Notes Series in Mathematics 10, 2010, pp. 281-371.

24. A note on restriction theorems for semistable sheaves, Math. Res. Lett. 17 (2010), 823-832, published version

25. Moduli spaces of framed perverse instantons on P³, with M. Hauzer, Glasgow Math. J. 53 (2011), 51-96, published version

26. On the S-fundamental group scheme, Ann. Inst. Fourier 61 (2011), 2077-2119, published version, arXiv version

27. On the S-fundamental group scheme II, J. Inst. Math. Jussieu 11 (2012), 835-854, a pdf file of the published version

28. On a positive equicharacteristic variant of the p-curvature conjecture, with H. Esnault, Doc. Math. 18 (2013), 23-50, published version (open access)

29. Moduli spaces of principal bundles on singular varieties, Kyoto J. Math. 53 (2013), 3-23, published version

30. Nef line bundles over finite fields, Int. Math. Res. Not. 2013 (2013), (15): 3490-3508, published version

31. On positivity and semistability of vector bundles in finite and mixed characteristics, J. Ramanujan Math. Soc. 28A (Special Issue-2013), 287-309, arXiv version

32. Semistable modules over Lie algebroids in positive characteristic, Doc. Math. 19 (2014), 509-540, published version (open access)

33. Bogomolov's inequality for Higgs sheaves in positive characteristic, Invent. Math. 199 (2015), 889-920, published version (open access)

34. Generic positivity and foliations in positive characteristic, Adv. Math. 277 (2015), 1-23, published version, a pdf file

35. The Bogomolov-Miyaoka-Yau inequality for logarithmic surfaces in positive characteristic, Duke Math. J. 165 (2016), 2737-2769, published version

36. Rank 3 rigid representations of projective fundamental groups, with C. Simpson, Compositio Math. 154 (2018), 1534-1570, published version, arXiv version

37. Lifting zero-dimensional schemes and divided powers, Bull. Lond. Math. Soc. 50 (2018), 449-461, published version, arXiv version

38. Birational geometry of compactifications of Drinfeld half-spaces over a finite field, Adv. Math. 345 (2019), 861-908, published version, arXiv version

39. On birational boundedness of foliated surfaces, with Ch. Hacon, J. Reine Angew. Math. 770 (2021), 205-229, published version, arXiv version

40. On smooth projective D-affine varieties, Int. Math. Res. Not. 15 (2021), 11889-11922, published version, arXiv version

41. Nearby cycles and semipositivity in positive characteristic, J. Eur. Math. Soc. 24 (2022), 3829-3872, published version (open access), arXiv version

42. On boundedness of semistable sheaves, Doc. Math. 27 (2022), 1-16, published version (open access), arXiv version, erratum

43. Positivity vs. slope semistability for bundles with vanishing discriminant, with M. Fulger, J. Algebra 609 (2022), 657-687, published version (open access), arXiv version

44. On algebraic Chern classes of flat vector bundles, Manuscripta Math. 174 (2024), 1-29, published version (open access), arXiv version (old version)

45. Bogomolov's inequality and Higgs sheaves on normal varieties in positive characteristic, J. Reine Angew. Math. 810 (2024), 1-48, published version (open access), arXiv version (extended but in need of small corrections)

46. Bridgeland stability conditions on normal surfaces, Ann. Mat. Pura Appl. 203 (2024), 2653-2664, published version (open access), arXiv version, preprint (2023)

47. Approximation of semistable bundles on smooth algebraic varieties, J. Algebra 664 (2025), 655-670, published version, open access version (till 19.12.2024) , arXiv version

48. Moduli spaces of semistable modules over Lie algebroids, 34 pages, arXiv version, preprint (2021)

49. Intersection theory and Chern classes on normal varieties, 45 pages, arXiv version, preprint (2022)

50. Simpson's correspondence on singular varieties in positive characteristic, 62 pages, arXiv version, preprint (2023)

51. Projective contact log varieties, 52 pages, arXiv version, preprint (2024)

Other papers:

1. Notes from a lecture by F. Hirzebruch: Complex cobordism and the elliptic genus, Contemp. Math. 241 (1999), 9-20.

2. Langlands program according to Lafforgue, (in Polish), Wiadom. Mat. 39 (2003), 39-46, a pdf file

Edited books:

1. String-Math 2022, Eds. Ron Donagi, Adrian Langer, Piotr Sulkowski, Katrin Wendland, Proc. Symp. Pure Math. 107 (2024).