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On the notion of canonical dimension for algebraic groups
Grégory Berhuy,Zinovy Reichstein +1 more
TLDR
In this article, the canonical dimension of an algebraic group action is defined and studied, and the problem of computing the minimal number of parameters required to define a generic hypersurface of degree d in P^{n-1}.Abstract:
We define and study a new numerical invariant of an algebraic group action which we call the canonical dimension. We then apply the resulting theory to the problem of computing the minimal number of parameters required to define a generic hypersurface of degree d in P^{n-1}.read more
Citations
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Book
The Algebraic and Geometric Theory of Quadratic Forms
TL;DR: The classical theory of symmetric bilinear forms and quadratic forms: Bilinear form Quadratic form forms over rational function fields Function fields of quadrics Bilinverse forms and algebraic extensions $u$-invariants Applications of the Milnor conjecture on the norm residue homomorphism of degree two Algebraic cycles: Homology and cohomology Chow groups Steenrod operations Category of Chow motives Quadratically forms and cyclic cycles as mentioned in this paper.
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Essential dimension of finite p -groups
TL;DR: In this article, it was shown that the essential dimension and p-dimension of a p-group G over a field F containing a primitive p-th root of unity is equal to the least dimension of a faithful representation of G over F.
Journal ArticleDOI
Canonical p-dimension of algebraic groups
TL;DR: In this article, the p-relative version of the Berhuy-Reichstein canonical dimension for an algebraic group over an arbitrary field of an arbitrary characteristic (p is any prime integer) is presented.
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Essential dimension: a survey
TL;DR: In this article, a survey of the literature on the essential dimension of finite groups, groups of multiplicative type and the spinor groups is presented, along with self-contained proofs of these cases and applications in the theory of simple algebras.
Journal Article
On the Chow Groups of Quadratic Grassmannians
TL;DR: In this article, the Chow-ring of the Grassmanian of the middle-dimensional planes on arbi- trary projective quadric is described and a conjecture describing the canonical dimension of the quadric Q in terms of J(Q) is formulated.
References
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Book
Linear Algebraic Groups
TL;DR: A survey of rationality properties of semisimple groups can be found in this paper, where a survey of rational properties of algebraic groups is also presented, as well as a classification of reductive groups representations.
Book
The Book of Involutions
TL;DR: A comprehensive exposition of the theory of central simple algebras with involution, in relation with linear algebraic groups is given in this article, which provides the algebra-theoretic foundations for much of the recent work on linear algebraIC groups over arbitrary fields.