Essential dimension of sequences of quadratic Pfister forms
Abstract
We study the essential dimension of m m -tuples ( φ 1 , … , φ m ) (\varphi _1,\dots ,\varphi _m) of quadratic n n -fold Pfister forms over a field F F such that the Witt class of φ 1 ⊥ … ⊥ φ m \varphi _1 \perp \ldots \perp \varphi _m lies in I q n + 1 F I_q^{n+1}F . We show that the essential dimension is equal to n + 1 n+1 when m = 3 m=3 , and is either 4 4 or 5 5 when n = 2 = c h a r k n=2=\mathsf {char}k and m = 4 m=4 .
Fields of Study & Subjects
Algebraic Geometry and Number Theory
Advanced Algebra and Geometry
Rings
Modules
and Algebras
Publication details
- Journal / source
- Proceedings of the American Mathematical Society
- Volume
- 154
- Issue
- 6
- Pages
- 2337–2344
- Publication date
- 13 March 2026
- Language
- EN