Geodesic
Projective bundle theorem in MW-motivic cohomology
Documenta mathematica, Tome 26 (2021), pp. 1045-1083.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

We present a version of projective bundle theorem in MW-motives (resp. Chow-Witt rings), which says that $\widetilde{CH}^*(\mathbb{P}(E))$ is determined by $\widetilde{CH}^*(X), \widetilde{CH}^*(X,det(E)^{\vee}), CH^*(X)$ and $Sq^2$ for smooth quasi-projective schemes $X$ and vector bundles $E$ over $X$ with $e(E^{\vee})=0\in H^n(X,W(det(E)))$, provided that $_2CH^*(X)=0$. \par As an application, we compute the MW-motives of blow-ups with smooth centers. Moreover, we discuss the invariance of Chow-Witt cycles of projective bundles under automorphisms of vector bundles.
Classification : 14F42, 11E81, 19
Keywords: MW-motivic cohomology, Chow-Witt ring, projective bundle theorem 
@article{DOCMA_2021__26__a29,
     author = {Yang, Nanjun},
     title = {Projective bundle theorem in {MW-motivic} cohomology},
     journal = {Documenta mathematica},
     pages = {1045--1083},
     publisher = {mathdoc},
     volume = {26},
     year = {2021},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DOCMA_2021__26__a29/}
}
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Yang, Nanjun. Projective bundle theorem in MW-motivic cohomology. Documenta mathematica, Tome 26 (2021), pp. 1045-1083. http://geodesic.mathdoc.fr/item/DOCMA_2021__26__a29/