A Historical background....................................... xi A. 1 The conjectural theory described by
Beilinson............ xi A. 2 Voevodsky's motivic complexes........................ xii A. 3 Morel and …

We establish a general “affine representability” result in A 1-homotopy theory over a general
base. We apply this result to obtain representability results for vector bundles in A 1 …

In this book we prove (Thm. 4. 3.24) unified classification results for stable equivariant Γ-
principal bundles when the underlying homotopy type SΓ of the topological structure group Γ …

Let $ S $ be a Noetherian scheme of finite dimension and denote by $\unicode
[STIX]{x1D70C}\in [\unicode [STIX]{x1D7D9},\mathbb {G} _ {m}] _ {\mathbf {SH}(S)} $ the …

The concept of orbifolds should unify differential geometry with equivariant homotopy theory,
so that orbifold cohomology should unify differential cohomology with proper equivariant …

In this work we develop a theory of motives for logarithmic schemes over fields in the sense
of Fontaine, Illusie, and Kato. Our construction is based on the notion of finite log …

Simplicial presheaves on cartesian spaces provide a general notion of smooth spaces.
There is a corresponding smooth version of the singular complex functor, which maps …

We extend the Chern character on K-theory, in its generalization to the Chern-Dold
character on generalized cohomology theories, further to (twisted, differential) non-abelian …

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 …

We show that all extended functorial field theories, both topological and nontopological, are
local. We define the smooth (infinity, d)-category of bordisms with geometric data, such as …