Steenrod operations in chow theory
TLDR
An action of the Steenrod algebra is constructed on the mod p Chow theory of varieties over a field of characteristic different from p, answering a question posed in Fulton's intersection theory.Abstract:
An action of the Steenrod algebra is constructed on the mod p Chow theory of varieties over a field of characteristic different from p, answering a question posed in Fulton's Intersection Theory. The action agrees with the action of the Steenrod algebra used by Voevodsky in his proof of the Milnor conjecture. However, the construction uses only basic functorial properties of equivariant intersection theory.read more
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The Algebraic and Geometric Theory of Quadratic Forms
TL;DR: The classical theory of symmetric bilinear forms and quadratic forms: Bilinear form Quadratic form forms over rational function fields Function fields of quadrics Bilinverse forms and algebraic extensions $u$-invariants Applications of the Milnor conjecture on the norm residue homomorphism of degree two Algebraic cycles: Homology and cohomology Chow groups Steenrod operations Category of Chow motives Quadratically forms and cyclic cycles as mentioned in this paper.
Journal ArticleDOI
Hirzebruch classes and motivic chern classes for singular spaces
TL;DR: In this paper, a new theory of characteristic homology classes of singular complex algebraic spaces was introduced, which generalizes the total λ-class λy(T*X) of the cotangent bundle to singular spaces.
Posted Content
Hirzebruch classes and motivic Chern classes for singular spaces
TL;DR: In this article, a new theory of characteristic homology classes for singular complex algebraic spaces was introduced, which generalizes the total \lambda-class of the cotangent bundle to singular spaces.
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J-invariant of linear algebraic groups
TL;DR: In this paper, the authors introduce le J-invariant de G which caracterises le comportement motivique de X and generalise le J invariant defini par A. Vishik dans le cadre des formes quadratiques.
References
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Journal ArticleDOI
The irreducibility of the space of curves of given genus
Pierre Deligne,David Mumford +1 more
TL;DR: In this article, the authors implique l'accord avec les conditions generales d'utilisation (http://www.numdam.org/legal.php).
Journal ArticleDOI
Equivariant intersection theory (With an Appendix by Angelo Vistoli: The Chow ring of M2)
Dan Edidin,William Graham +1 more
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Versal Deformations and Algebraic Stacks
TL;DR: In this article, a review of Schlessinger's conditions is presented, and a reduction of a flat groupoid to an algebraic stack is discussed. But it is not discussed in this paper.
Journal ArticleDOI
Reduced power operations in motivic cohomology
TL;DR: In this paper, an analog of Steenrod operations in motivic cohomology was constructed and the Cartan formula, the Adem relations and the realtions to characteristic classes were proved.
Book ChapterDOI
The Chow Ring of a Classifying Space
TL;DR: The Chow ring of the classifying space of a linear algebraic group is defined in this paper, which is a topological invariant for the Hodge conjecture with integer coefficients.