Modules over motivic cohomology

By O. Rondigs, P. Østvær. 2008

119 citations recorded by the source corpus.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/41859df7bd8e438b6823a7e0d660f9f07fb2c35a

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In Geometry and Topology

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Citations in the corpus

The homotopy coniveau tower (2005, methodology): “For the results on DM(k) and SH(k) we use in this section, we refer the reader to the lectures of Morel [12, 13] and Voevodsky [23], as well as the papers of Ostvar-Roendigs [ 15 , 17] and Spitzweck [18].”
Motivic slices and coloured operads (2010, methodology): “re highly structured E-modules. When the base scheme is a ﬁeld of characteristic zero, it follows that the slices are motives, i.e. strict modules over the motivic Eilenberg-MacLane spectrum MZ [25], [26]. However, in general, the techniques in [23] appear to be impractical to answer questions conce”
A comparison of motivic and classical stable homotopy theories (2011, background): “Röndigs-Østvær [30] consider the categoryChSS P1 of symmetric Z (P(1)∗)-spectra in (unbounded) chain complexes of presheaves with transfer on Sm/k.”
La réalisation étale et les opérations de Grothendieck (2014, background): “Dans [41], les auteurs suivent de plus près la recette de Jardine [27] consistant à prendre des T -spectres à valeurs dans des catégories de modèles instables.”
The motive of a classifying space (2014, methodology): “Following Röndigs and Østvær, the triangulated category DMT (k;R) of mixed Tate motives with coefficients in R is the smallest localizing subcategory of DM(k;R) that contains R(j) for all integers j [47].”
Slices of hermitian $K$–theory and Milnor's conjecture on quadratic forms (2013, background): “MZ/ DMZ: It follows that smashing with MZ, ie passing to motives [45; 46], induces a canonical ring map Œ1; 1 ! Œs0.”
The first stable homotopy groups of motivic spheres (2016, background): “The module theory of motivic cohomology in relation to motives was worked out in [59] and [60].”
Mixed Weil cohomologies (2007, background): “1) is proved in [53] using resolution of singularities by de Jong alterations [17]; however, it will be shown in [15] that such an equivalence of triangulated categories holds over a geometrically unibranch base scheme, by very different methods (without using any kind of resolution of singularities”