Homepage von Kay Rülling

Adresse

Vorlesungen

• Cohomology of sheaves on schemes, SoSe 19, an der TU München.
• Algberaic curves and the Weil conjectures, SoSe 19, an der TU München.
• The de Rham-Witt complex , WiSe 18/19, an der FU Berlin.
• Algebra und Zahlentheorie , WiSe 17/18, an der FU Berlin.
• Algebra II , WiSe 16/17, an der HU Berlin.
• Weil Conjecture for curves, WiSe 16/17, an der HU Berlin.
• Elliptic Curves , WiSe 15/16.
• Number Theory 3 , WiSe 14/15.

Seminare

• Topological Hochschild Homology and the de Rham-Witt complex, mit Holger Reich, Forschungsseminar Arithmetik und Topologie Reich, WiSe15/16.
• Supersingular K3 surfaces are unirational (following C. Liedtke), Research Seminar Esnault, WiSe15/16.
• Semistable Reduction & Unimodular Triangulations mit Christian Haase und Lars Kastner, Seminar Polytopes and Algebraic Geometry Haase, SoSe15.

Veröffentlichungen

1. The generalized de Rham-Witt complex over a field is a complex of zero-cycles .
   J. Algebr. Geom. 16, No. 1 (2007), 109-169.
   
   
2. (mit Andre Chatzistamatiou) Higher direct images of the structure sheaf in positive characteristic.
   Algebra & Number Theory, vol 5, No. 6 (2011), 693-775. http://arxiv.org/abs/0911.3599
   
   
3. (mit Pierre Berthelot, Hélène Esnault) Rational points over finite fields for regular models of algebraic varieties of Hodge type ≥ 1.
   Annals of Mathematics, vol 176, No. 1 (2012), 413-508. http://arxiv.org/abs/1009.0178
   
   
4. (mit Andre Chatzistamatiou) Hodge-Witt Cohomology and Witt-rational singularities.
   Documenta Mathematica, vol 17 (2012), 663-781.
   
   
5. (mit Takao Yamazaki) A vanishing result for a K-group of reciprocity functors.
   Journal of K-theory, vol 14, issue 03 (2014), 556-569. https://arxiv.org/pdf/1312.4205.pdf.
   
   
6. (mit Andre Chatzistamatiou) Vanishing of the higher direct images of the structure sheaf.
   Compositio Mathematica, vol 151, issue 11 (2015), 2131-2144. https://arxiv.org/abs/1404.1827
   
   
7. (mit Florian Ivorra) K-groups of reciprocity functors.
   J. Algebraic Geom. 26, No. 2 (2017), 199-278. http://arxiv.org/abs/1209.1217
   
   
8. (mit Takao Yamazaki) Suslin homology of relative curves with modulus.
   Journal of the London Mathematical Society 2016; doi: 10.1112/jlms/jdw006
   
   
9. Kähler differentials and de Rham-Witt differentials have reciprocity.
   7 pages. Appendix to "Reciprocity sheaves, I" by Bruno Kahn, Shuji Saito, Takao Yamazaki.
   Compositio Mathematica, vol 152, issue 9 (2016), 1851-1898. http://arxiv.org/abs/1402.4201
   
   
10. (mit Shuji Saito) Higher Chow groups with modulus and relative Milnor K-theory.
    Trans. Amer. Math. Soc. 370 (2018), pp. 987-1043. http://arxiv.org/abs/1504.02669
    
    

Vorveröffentlichungen

11. (mit Shuji Saito) Reciprocity sheaves and abelian ramification theory.
    83 pages, preprint 2018, https://arxiv.org/abs/1812.08716.
    
    

Übersichtsartikel

• (mit Lars Kindler) Introductory course on l-adic sheaves and their ramification theory on curves.
  To appear in Clay Mathematics Proceedings, Periods and Motives: Feynman Amplitudes in the 21st Century.
  These are notes for students without any original mathematical content, see http://arxiv.org/abs/1409.6899.
  
  
• (mit Manuel Blickle, Hélène Esnault) Characteristic 0 and p analogies, and some motivic cohomology.
  Global aspects of complex geometry, Springer, Berlin (2006), 59-82. http://arxiv.org/abs/math/0512190
  
  

Errata

• Erratum to " The generalized de Rham-Witt complex over a field is a complex of zero-cycles ". J. Algebr. Geom. 16, No. 4, 793-795 (2007).
• A small Erratum to " Higher direct images of the structure sheaf in positive characteristic ".
  One formula is corrected, it does not effect any results or proofs of the article.

Diverses

• Reciprocity sheaves and abelian ramification theory.
  This is a version of my contribution to the Oberwolfach Report No. 29/2019, Algebraic K-theory, organized by T. Geisser, L. Hesselholt, A. Huber-Klawitter, M.Kerz.
  It essentially is an overview of the article 11 from above.
  
  
• Vanishing of Witt vector cohomology and action of correspondences.
  This is essentially the introduction of my Habilitation thesis (up to some small changes) and as such is an overview of the articles 2- 4, 7 from above.
  The perspective from the introductions of the respective articles is slightly changed. But there is no originalitiy in these notes. 22 pages (2013).