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Bulletin of the American Mathematical Society

Published by the American Mathematical Society, the Bulletin of the American Mathematical Society (BULL) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-9485 (online) ISSN 0273-0979 (print)

The 2020 MCQ for Bulletin of the American Mathematical Society is 0.47.

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Essential dimension
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by Alexander S. Merkurjev PDF
Bull. Amer. Math. Soc. 54 (2017), 635-661 Request permission


In this paper we survey research on the essential dimension that was introduced by J. Buhler and Z. Reichstein. Informally speaking, the essential dimension of a class of algebraic objects is the minimal number of algebraically independent parameters one needs to define any object in the class. The notion of essential dimension, which is defined in elementary terms, has surprising connections to many areas of algebra, such as algebraic geometry, algebraic $K$-theory, Galois cohomology, representation theory of algebraic groups, theory of fibered categories and valuation theory. The highlights of the survey are the computations of the essential dimensions of finite groups, groups of multiplicative type and the spinor groups.
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Additional Information
  • Alexander S. Merkurjev
  • Affiliation: Department of Mathematics, University of California at Los Angeles, Los Angeles, California 90095-1555
  • MR Author ID: 191878
  • ORCID: 0000-0002-4447-1838
  • Email:
  • Received by editor(s): October 17, 2016
  • Published electronically: December 19, 2016
  • Additional Notes: The work has been supported by the NSF grant DMS #1160206
  • © Copyright 2016 American Mathematical Society
  • Journal: Bull. Amer. Math. Soc. 54 (2017), 635-661
  • MSC (2010): Primary 14L30, 20G10, 11E72
  • DOI:
  • MathSciNet review: 3683628