Geodesic
Gersten complex for sheaves with transfers for noetherian schemes
Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, no. 6 (2015), pp. 98-101 Cet article a éte moissonné depuis la source Math-Net.Ru

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V. Voevodsky introduced Gersten complex for sheaves with transfers in one of the first papers where the category of motives was constructed. Becides he proved Gersten conjecture which states that the Gersten complex for the local ring of point of smooth variety over field $k$ is resolution of the group of global sections over this ring. Because of this fundamental fact Gersten complex can be used for calculations of cohomologies of sheaves with transfers over smooth $k$-varieties. In this paper we construct Gersten complex for sheaves with transfers, which defined on the category of noetherian $k$-schemes, where $char~k=0$. After this we proof the Gersten conjecture in case of local noetherian ring over field $k$. This generalises Voevodsky's result.
Keywords: sheaf with transfer, Gersten conjecture, equicharacteristic ring, Voevodsky motives, transfer, noetherian scheme, blow up.
Mots-clés : Gysin homomorphism 
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     author = {A. A. Mingazov},
     title = {Gersten complex for sheaves with transfers for noetherian schemes},
     journal = {Vestnik Samarskogo universiteta. Estestvennonau\v{c}na\^a seri\^a},
     pages = {98--101},
     year = {2015},
     number = {6},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VSGU_2015_6_a12/}
}
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A. A. Mingazov. Gersten complex for sheaves with transfers for noetherian schemes. Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, no. 6 (2015), pp. 98-101. http://geodesic.mathdoc.fr/item/VSGU_2015_6_a12/

[1] Voevodsky V., Suslin A., Friedlander E., “Cohomological Theory of Presheves with Transfers”, Cycles, Transfers and Motivic Homology Theories, Annals of Math. Studies, 1999 | MR

[2] Panin I. A., “The Equicharacteristic Case of the Gersten Conjecture”, Theory of numbers, algebra and algebraic geometry, Collection of articles, Proceedings of Steklov Mathematical Institute, RAS, 241, Nauka, M., 2003, 169–178 (in English) | MR | Zbl

[3] Panin I., “Oriented Cohomology Theories of Algebraic Varieties”, K-Theory, 30:3, Special issue in honor of H. Bass on his seventieth birthday. Part III (2003), 265–314 | DOI | MR | Zbl

[4] Mingazov A. A., “Coherence of Gysin homomorphism and transfer”, Algebra and Analysis, 27:4 (2015), 59–73 (in Russian)

[5] Popesku D., “General Néron Desingularization”, Nagoya Math. J., 100 (1985), 97–126 | DOI | MR

[6] Levine M., “Oriented cohomology, Borel-Moore homology and algebraic cobordism”, Michigan Math. J., 57 (2008), 523–572 | DOI | MR | Zbl