An exact sequence for KM /2 ∗ with applications to quadratic forms By D. Orlov,∗ A. Vishik,∗∗ and V. Voevodsky∗∗* Contents 1. Introduction 2. An exact sequence for KM /2 ∗ 3. Reduction to points of degree 2 4. Some applications . Milnor’s Conjecture on quadratic forms . The Kahn-Rost-Sujatha Conjecture . The J-ﬁltration conjecture 1. Introduction Let k be a ﬁeld of characteristics zero. For a sequence a = (a1 , . . . , an ) of invertible elements of k consider the homomorphism M M K∗ (k)/2 → K∗+n (k)/2 in Milnor’s K-theory modulo elements divisible by 2 deﬁned by.