Duke Mathematical Journal

Motivic cohomology of the complement of hyperplane arrangements

Andre Chatzistamatiou

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text


We give a presentation of the motivic cohomology ring of the complement of a hyperplane arrangement considered as an algebra over the motivic cohomology of the ground field

Article information

Duke Math. J., Volume 138, Number 3 (2007), 375-389.

First available in Project Euclid: 18 June 2007

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 14F42: Motivic cohomology; motivic homotopy theory [See also 19E15]


Chatzistamatiou, Andre. Motivic cohomology of the complement of hyperplane arrangements. Duke Math. J. 138 (2007), no. 3, 375--389. doi:10.1215/S0012-7094-07-13831-6. https://projecteuclid.org/euclid.dmj/1182180651

Export citation


  • V. I. Arnol'D [Arnold], The cohomology ring of the group of dyed braids (in Russian), Mat. Zametki $\mathbf5$ (1969), 227--231.; English translation in Math. Notes $\mathbf5$ (1969), 138--140.
  • E. Brieskorn, Sur les groupes de tresses, Lecture Notes in Math. $\mathbf317$, Springer, Berlin, 1973, 21--44., Séminaire Bourbaki 1971/1972, no. 401.
  • A. Chatzistamatiou, Motivische Kohomologie von Komplementen von Konstellationen affiner Räume, Ph.D. dissertation, Universität Duisberg-Essen, Essen, Germany, 2006.
  • T. Ekedahl, ``On the adic formalism'' in The Grothendieck Festschrift, Vol. II, Progr. Math. $\mathbf87$, Birkhäuser, Boston, 1990, 197--218.
  • A. Huber, Realization of Voevodsky's motives, J. Algebraic Geom. $\mathbf9$ (2000), 755--799.; Corrigendum, J. Algebraic Geom. $\mathbf13$ (2004), 195--207.
  • F. Ivorra, Réalisation $l$-adique des motifs mixtes, C. R. Acad. Sci. Paris $\mathbf342$ (2006), 505--510.
  • J. Milnor, Algebraic $K$-theory and quadratic forms, Invent. Math. $\mathbf9$ (1969/1970), 318--344.
  • P. Orlik and L. Solomon, Combinatorics and topology of complements of hyperplanes, Invent. Math. $\mathbf56$ (1980), 167--189.
  • A. Suslin and V. Voevodsky, ``Bloch-Kato conjecture and motivic cohomology with finite coefficients'' in The Arithmetic and Geometry of Algebraic Cycles (Banff, Canada, 1998), NATO Sci. Ser. C Math. Phys. Sci. 548, Kluwer, Dordrecht, Netherlands, 2000, 117--189.
  • V. Voevodsky, ``Triangulated category of motives over a field'' in Cycles, Transfers, and Motivic Homology Theories, Ann. of Math. Stud. $\mathbf143$, Princeton Univ. Press, Princeton, 2000, 188--238.
  • —, Cancellation theorem, preprint,\arxivmath/0202012v1[math.AG]