Modules de cycles et classes non ramifi\'ees sur un espace classifiant

@article{Kahn2012ModulesDC,
  title={Modules de cycles et classes non ramifi\'ees sur un espace classifiant},
  author={Bruno Kahn and Ngan Thi Kim Nguyen},
  journal={arXiv: Algebraic Geometry},
  year={2012}
}
Let G be a finite group of exponent m and let k be a field of characteristic prime to m, containing the m-th roots of unity. For any Rost cycle module M over k, we construct exact sequences detecting the unramified elements in Serre's group of invariants of G with values in M in terms of "residue" morphisms associated to pairs (D,g), where D runs through the subgroups of G and g runs through the homomorphisms \mu_m \to G whose image centralises D. This allows us to recover results of Bogomolov… 
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References

SHOWING 1-10 OF 64 REFERENCES
Unramified elements in cycle modules
Let X be an algebraic variety over a field F. We study the functor taking a cycle module M over F to the group of unramified elements M(F(X))nr of M(F(X)). We prove that this functor is represented
APPLICATION OF MOTIVIC COMPLEXES TO NEGLIGIBLE CLASSES
Lichtenbaum's complex enables one to relate Galois cohomology to K ­cohomo­ logy groups. In this paper, we consider the first terms of the Hochschild­Serre spectral sequence for the cohomology of
Unramified cohomology of degree 3 and Noether’s problem
Let G be a finite group and W be a faithful representation of G over C. The group G acts on the field of rational functions C(W). The question whether the field of invariant functions C(W)G is purely
The rationality problem for fields of invariants under linear algebraic groups (with special regards to the Brauer group)
This is a survey on the ancient question : Let G be a reductive group over an algebraically closed field k and let V be a vector space over k with an almost free linear action of G on V. Let k(V)
The Chow ring of a classifying space
We define the Chow ring of the classifying space of a linear algebraic group. In all the examples where we can compute it, such as the symmetric groups and the orthogonal groups, it is isomorphic to
STABLE COHOMOLOGY OF GROUPS AND ALGEBRAIC VARIETIES
The notion of stable cohomology of algebraic varieties and, based on it, the analogous concept for finite and profinite groups are introduced. It is proved that the ordinary and stable cohomology
Birational Geometry and Localisation of Categories
We explore connections between places of function fields over a base field F and birational morphisms between smooth F- varieties. This is done by considering various categories of fractions
Motivic cohomology groups are isomorphic to higher chow groups in any characteristic
In this short paper we show that the motivic cohomology groups defined in [3] are isomorphic to the motivic cohomology groups defined in [1] for smooth schemes over any field. In view of [1,
A SPECTRAL SEQUENCE FOR MOTIVIC COHOMOLOGY
We show that, assuming a rather innocuous looking ”moving lemma” called Theorem A, this complex is an exact couple, and the resulting spectral sequence has the form (0.1.1). §2 §6 of the paper are
Applications of Weight-two Motivic Cohomology
Using Lichtenbaum's complex (2), we reprove and extend a little bit some known results relating the kernel of H 3 (F;Q=Z(2)) ! H 3 (F (X);Q=Z(2)) to the torsion of CH 2 X for rational varieties X .
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