We establish a relative version of the abstract “affine representability” theorem in A 1–
homotopy theory from part I of this paper. We then prove some A 1–invariance statements for …

The first stable homotopy groups of motivic spheres Page 1 Annals of Mathematics 189 (2019),
1–74 https://doi.org/10.4007/annals.2019.189.1.1 The first stable homotopy groups of motivic …

This work is dedicated to the construction of a new motivic homotopy theory for (log)
schemes, generalizing Morel-Voevodsky's (un) stable $\mathbb {A}^ 1$-homotopy category …

We determine the first non-stable-homotopy sheaf of. Using techniques of obstruction theory
involving the-Postnikov tower, supported by some ideas from the theory of unimodular rows …

We establish the equality of two definitions of a Euler class in algebraic geometry: the first
definition is as a 'characteristic class' with values in Chow–Witt theory, while the second …

We give a cohomological classification of vector bundles of rank 2 on a smooth affine
threefold over an algebraically closed field having characteristic unequal to 2. As a …

We show that the higher Grothendieck–Witt groups, aka algebraic hermitian K K-groups, are
represented by an infinite orthogonal Grassmannian in the A^ 1 A 1-homotopy category of …

We study maps from a smooth scheme to a motivic sphere in the Morel–Voevodsky A1-
homotopy category, ie, motivic cohomotopy sets. Following Borsuk, we show that, in the …

Abstract We introduce Milnor–Witt K-groups of local rings and show that the nth Milnor–Witt
K-group of a local ring R which contains an infinite field of characteristic not 2 is the pull …

We study a version of the James model for the loop space of a suspension in unstable A 1–
homotopy theory. We use this model to establish an analog of GW Whitehead's classical …