A note on generic splitting of quadratic forms

Abstract

Let F be a field of any characteristic. For n ≥ 0, let J(n) = {q̄ ∈ Wq(F)| deg(q) ≥ n}. The degree conjecture asserts that for each n ≥ 0 (DC) J(n) = InWq(F) Let p be any n-fold quadratic Pfister form over F and F(p) the function field of p. Then the function field conjecture asserts (FFC) ker [InWq(F)/In+1Wq(F) → InWq(F(p))/In+1Wq(F(p))] = {0, p̄} We prove that (DC) is equivalent to (FFC).