Essential dimension

Merkurjev, Alexander

doi:10.1090/bull/1564

Essential dimension
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by Alexander S. Merkurjev PDF

Bull. Amer. Math. Soc. 54 (2017), 635-661 Request permission

Abstract:

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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