Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



The index of a Brauer class on a Brauer-Severi variety

Authors: Aidan Schofield and Michel Van den Bergh
Journal: Trans. Amer. Math. Soc. 333 (1992), 729-739
MSC: Primary 12E15; Secondary 14M99, 16E20, 16K40
MathSciNet review: 1061778
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Let $ D$ and $ E$ be central division algebras over $ k$; let $ K$ be the generic splitting field of $ E$; we show that the index of $ D{ \otimes _k}K$ is the minimum of the indices of $ D \otimes {E^{ \otimes i}}$ as $ i$ varies. We use this to calculate the index of $ D$ under related central extensions and to construct division algebras with special properties.

References [Enhancements On Off] (What's this?)

  • [1] M. Artin (Notes by A. Verschoren), Brauer-Severi varieties, Lecture Notes in Math., vol. 917, Springer-Verlag, 1981, pp. 194-210. MR 657430 (83j:14015)
  • [2] A. Blanchet, Function fields of generalized Brauer-Severi varieties, preprint, University of Nebraska, 1989. MR 1092553 (92c:14052)
  • [3] R. Hartshorne, Algebraic geometry, Graduate Texts in Math., no. 52, Springer-Verlag, New York, 1977. MR 0463157 (57:3116)
  • [4] S. Lichtenbaum, The period-index problem for elliptic curves, Amer. J. Math. 90 (1968), 1209-1223. MR 0237506 (38:5788)
  • [5] J. S. Milne, Étale cohomology, Princeton Univ. Press, Princeton, N. J., 1980. MR 559531 (81j:14002)
  • [6] D. Quillen, Higher algebraic $ K$-theory. I, Lecture Notes in Math., vol. 341, Springer-Verlag, 1972, pp. 85-147. MR 0338129 (49:2895)
  • [7] A. Schofield and M. Van den Bergh, Division algebra coproducts of index $ n$, Trans. Amer. Math. Soc. (to appear).
  • [8] J. Tignol and A. Wadsworth, Totally ramified valuations on finite-dimensional division algebras, Trans. Amer. Math. Soc. 302 (1987), 223-250. MR 887507 (88j:16025)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 12E15, 14M99, 16E20, 16K40

Retrieve articles in all journals with MSC: 12E15, 14M99, 16E20, 16K40

Additional Information

Article copyright: © Copyright 1992 American Mathematical Society

American Mathematical Society