Essential dimension

Alexander S. Merkurjev
2016 Bulletin of the American Mathematical Society  
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,
more » ... ion 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.
doi:10.1090/bull/1564 fatcat:yyce3plsozfubfs6ijqe6u2ghy