Nonexcellence of the Function Field of a Product of Conics with Common Quadratic Splitting Field

Abstract

As a complement to the article [4], for any m ≥ 2 we give examples of conics X ₁,…, X _m over a field F having a common quadratic splitting field extension and such that the extension F(X ₁ × … ×X _m )/F is not 8-excellent.

Key Words:

• Conic
• Laurent series field
• Pfister form

2000 Mathematics Subject Classification:

• 11E04
• 19D55

Notes

Communicated by A. Wadsworth.