An official website of the United States government
Abstract We determine the mod $$p$$ cohomological invariants for several affine group schemes $$G$$ in characteristic $$p$$. These are invariants of $$G$$-torsors with values in étale motivic cohomology, or equivalently in Kato’s version of Galois cohomology based on differential forms. In particular, we find the mod 2 cohomological invariants for the symmetric groups and the orthogonal groups in characteristic 2, which Serre computed in characteristic not 2. We also determine all operations on the mod $$p$$ étale motivic cohomology of fields, extending Vial’s computation of the operations on the mod $$p$$ Milnor K-theory of fields.
more »
« less
Note: When clicking on a Digital Object Identifier (DOI) number, you will be taken to an external site maintained by the publisher.
Some full text articles may not yet be available without a charge during the embargo (administrative interval).
What is a DOI Number?
Some links on this page may take you to non-federal websites. Their policies may differ from this site.
-
-
null (Ed.)Abstract We show that if X is a smooth complex projective surface with torsion-free cohomology, then the Hilbert scheme $$X^{[n]}$$ has torsion-free cohomology for every natural number n . This extends earlier work by Markman on the case of Poisson surfaces. The proof uses Gholampour-Thomas’s reduced obstruction theory for nested Hilbert schemes of surfaces.more » « less
-
We show that the subcategory of mixed Tate motives in Voevodsky’s derived category of motives is not closed under infinite products. In fact, the infinite product $$\prod _{n=1}^{\infty }\mathbf{Q}(0)$$ is not mixed Tate. More generally, the inclusions of several subcategories of motives do not have left or right adjoints. The proofs use the failure of finite generation for Chow groups in various contexts. In the positive direction, we show that for any scheme of finite type over a field whose motive is mixed Tate, the Chow groups are finitely generated.more » « less
-
null (Ed.)The Hilbert scheme $$X^{[a]}$$ of points on a complex manifold $$X$$ is a compactification of the configuration space of $$a$$ -element subsets of $$X$$ . The integral cohomology of $$X^{[a]}$$ is more subtle than the rational cohomology. In this paper, we compute the mod 2 cohomology of $$X^{[2]}$$ for any complex manifold $$X$$ , and the integral cohomology of $$X^{[2]}$$ when $$X$$ has torsion-free cohomology.more » « less
