Essential dimension of quadrics

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Essential dimension: a survey (2013, background): “It is shown in [45] (if char(F ) ̸= 2) and in [99] (if char(F ) = 2) that X is strongly 2-incompressible if and only if i1(X) = 1.”
Essential dimension of finite p-groups (2008, unknown): “[10]).”
Canonical p-dimension of algebraic groups (2006, background): “The computation of cd(X) for an anisotropic smooth projective quadric X (over a field of characteristic = 2), given in [12] (see Example 2.2), shows in fact also that cd 2 (X) = cd(X).”
Isotropy of quadratic forms over the function field of a quadric in characteristic 2 (2006, background): “Recall that in characteristic different from 2, the result [9, Th. 1] is also a consequence of Rost's degree formula [23], or of the very general results by Karpenko [15] on the first Witt index of quadratic forms and by Karpenko and Merkurjev on the essential dimension of quadrics [16].”
The Algebraic and Geometric Theory of Quadratic Forms (2008, background): “The results of this chapter for the case that characteristic 6= 2 were obtained in [76].”