• Corpus ID: 118046155

Lecture Notes On Motivic Cohomology

@inproceedings{Mazza2006LectureNO,
  title={Lecture Notes On Motivic Cohomology},
  author={Carlo Mazza and Vladimir Voevodsky and Charles A. Weibel},
  year={2006}
}
* Etale motivic theory: * Etale sheaves with transfers * The relative Picard group and Suslin's rigidity theorem * Derived tensor products $\mathbb{A}^1$-weak equivalence * Etale motivic cohomology and algebraic singular homology * Nisnevich sheaves with transfers: * Standard triples * Nisnevich sheaves* * Nisnevich sheaves with transfers * The triangulated category of motives: * The category of motives * The complex $\mathbb{Z}(n)$ and $\mathbb{P}^n$ Equidimensional cycles * Higher Chow groups… 
math.rutgers.edu
331 Citations
Highly Influential Citations
20
Background Citations
74
Methods Citations
26
Results Citations
3

331 Citations

Citation Type

Citation Type

On Chow-Weight Homology of Motivic Complexes and Its Relation to Motivic Homology
We study in detail the so-called Chow-weight homology of Voevodsky motivic complexes and relate it to motivic homology. We generalize earlier results and prove that the vanishing of higher motivic…
Thom isomorphisms in triangulated motivic categories
We show that a triangulated motivic category admits categorical Thom isomorphisms for vector bundles with an additional structure if and only if the generalized motivic cohomology theory represented…
Framed and MW-transfers for homotopy modules
In the paper we use the theory of framed correspondences to construct Milnor–Witt transfers on homotopy modules. As a consequence we identify the zeroth stable $${\mathbb {A}}^1$$A1-homotopy sheaf of…
Motivic spectral sequence for relative homotopy K-theory
We construct a motivic spectral sequence for the relative homotopy invariant K-theory of a closed immersion of schemes $D \subset X$. The $E_2$-terms of this spectral sequence are the…
Motivic cohomology of semistable varieties
We construct log-motivic cohomology groups for semistable varieties and study the p-adic deformation theory of log-motivic cohomology classes. Our main result is the deformational part of a p-adic…
A commutative P^1-spectrum representing motivic cohomology over Dedekind domains
We construct a motivic Eilenberg-MacLane spectrum with a highly structured multiplication over smooth schemes over Dedekind domains which represents Levine's motivic cohomology. The latter is defined…
Algebraic Cobordism and Étale Cohomology
Thomason's \'{e}tale descent theorem for Bott periodic algebraic $K$-theory \cite{aktec} is generalized to any $MGL$ module over a regular Noetherian scheme of finite dimension. Over arbitrary…
Mixed motives and geometric representation theory in equal characteristic
Let $$\mathbb {k}$$k be a field of characteristic p. We introduce a formalism of mixed sheaves with coefficients in $$\mathbb {k}$$k and apply it in representation theory. We construct a system of…
E-motives and motivic stable homotopy
We introduce in this work the notion of the category of pure $\mathbf{E}$-Motives, where $\mathbf{E}$ is a motivic strict ring spectrum and construct twisted $\mathbf{E}$-cohomology by using six…
On the Conservativity of Some Functors in Motivic Homotopy Theory
Given a 0-connective motivic spectrum $E \in SH(k)$ over a perfect field k, we determine $h_0$ of the associated motive $M E \in DM(k)$ in terms of $\pi_0 (E)$. Using this we show that if k has…
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References

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TLDR
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