Comparison of some field invariants. (English) Zbl 0972.11018
This paper deals with field invariants like Diophantine dimension, \(p\)-cohomological dimension, \(u\)-invariant (for \(p=2\)) and \(\lambda_p\)-invariant, i.e. the minimal number \(n\) such that every element \(c \in \text{Br}_p F\) is a sum of \(n\) classes of algebras of degree \(p\). Several interesting inequalities are derived, especially for the quadratic case \((p=2)\). Some of them depend on the Milnor Conjecture \(K^M (F)/2 = H^{\ast} (F, \mathbb{Z}/2)\). In an Appendix a result on divided powers in Milnor \(K\)-Theory is proved.
Reviewer: A.Pfister (Mainz)
MSC:
| 11E04 | Quadratic forms over general fields |
| 11E70 | \(K\)-theory of quadratic and Hermitian forms |
| 12G10 | Cohomological dimension of fields |
Keywords:
field invariant; Diophantine dimension; \(p\)-cohomological dimension; \(u\)-invariant; \(\lambda_p\)-invariant; Milnor conjectureReferences:
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