ﻻ يوجد ملخص باللغة العربية
We define push-forwards for Witt groups of schemes along proper morphisms, using Grothendieck duality theory. This article is an application of results of the authors on tensor-triangulated closed categories to such structures on some derived categories of schemes together with classical derived functors.
The paper provides computations of the first non-vanishing $mathbb{A}^1$-homotopy sheaves of the orthogonal Stiefel varieties which are relevant for the unstable isometry classification of quadratic forms over smooth affine schemes over perfect field
The Milnor conjecture has been a driving force in the theory of quadratic forms over fields, guiding the development of the theory of cohomological invariants, ushering in the theory of motivic cohomology, and touching on questions ranging from sums
We extend the big and $p$-typical Witt vector functors from commutative rings to commutative semirings. In the case of the big Witt vectors, this is a repackaging of some standard facts about monomial and Schur positivity in the combinatorics of symm
We provide a coherent overview of a number of recent results obtained by the authors in the theory of schemes defined over the field with one element. Essentially, this theory encompasses the study of a functor which maps certain geometries including
We compute Witt groups of maximal isotropic Grassmannians, aka. spinor varieties. They are examples of type D homogenuous varieties. Our method relies on the Blow-up setup of Balmer-Calm`es, and we investigate the connecting homomorphism via the proj