Quadratic forms in $I^n$ of dimension $2^n+2^{n-1}$ - Harvey, Curtis R.; Karpenko, Nikita A. (Comptes Rendus. Mathématique)
For $n\ge 3$, confirming a weak version of a conjecture of Hoffmann, we show that every anisotropic quadratic form in $I^n$ of dimension $2^n+2^{n-1}$ splits over a finite extension of the base field of degree not divisible by $4$. The first new case is $n=4$, where we obtain a classification of the corresponding quadratic forms up to odd degree base field extensions and get this way a strong upper bound on their essential $2$-dimension. As well, we compute the reduced Chow group of the maximal orthogonal grassmannian of the quadratic form and conclude that its canonical $2$-dimension is $2^n+2^{n-2}-2$.