Formally real fields with prescribed invariants in the theory of quadratic forms

Proceedings of the Conference on Quadratic Forms and Related Topics

“…In [M2], Merkurjev constructed to each n ≥ 1 fields with u(F ) = 2n and I 3 F = 0. It has been shown by Hornix [Hor,Th. 3.5] and Lam [L2] that for each n ≥ 3 there exist real fields F , F such that u(F ) = ũ(F ) = 2n and u(F ) + 2 = ũ(F ) = 2n.…”

A Collection of Manuscripts Written in Honour of Andrei A. Suslin on the Occasion of His Sixtieth Birthday

“…In fact, we know extremely little about fields with u(F ) < u(F ) < ∞. The only values which could be realized so far are fields where u(F ) = 2n and u(F ) = 2n + 2 for any n ≥ 2 (see [L2], [Hor2], [H3]), and fields with u(F ) = 8 and u(F ) = 12, see [H2,Cor. 6.4].…”