Higher Trace Forms and Essential Dimension in Central Simple Algebras
نویسنده
چکیده
We show that the essential dimension of a finite-dimensional central simple algebra coincides with the essential dimension of its rlinear trace form, (a1, . . . , ar) 7→ tr(a1 . . . ar), for any r ≥ 3.
منابع مشابه
Trace forms of central simple algebras over a local field or a global field
Introduction: Let A be a central simple algebra over a field k of characteristic different from 2. The quadratic form x ∈ A 7→ TrdA(x ) ∈ k is called the trace form of A, and is denoted by TA. This trace form has been studied by many authors (cf.[L], [LM], [Ti] et [Se], Annexe §5 for example). In particular, these classical invariants are well-known (loc.cit.). In [B], we have determined a diag...
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