Intersecting the dimension and slice filtrations for motives

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Intersecting the dimension and slice filtrations for motives. / Бондарко, Михаил Владимирович.

In: Homology, Homotopy and Applications, Vol. 20, No. 1, 2018, p. 259-274.

Research output: Contribution to journal › Article › peer-review

BibTeX

@article{ceb812a64763490aa6464841d0b8116f,

title = "Intersecting the dimension and slice filtrations for motives",

abstract = "In this note we prove that the intersections of the levels of the dimension filtration on Voevodsky's motivic complexes over a field with the levels of the slice filtration are {"}as small as possible{"}. This statement is applied to prove that a conjecture of Ayoub is equivalent to a certain orthogonality assumption.",

keywords = "Chow motive, Dimension filtration, Slice filtration, Triangulated category, Voevodsky motive, Weight structure",

author = "Бондарко, {Михаил Владимирович}",

note = "Funding Information: Research is supported by the Russian Science Foundation grant No. 16-11-10200. Received June 16, 2017, revised November 13, 2017; published on February 21, 2018. 2010 Mathematics Subject Classification: Primary: 14C15, 18E30. Secondary: 19E15, 14C25, 18E35. Key words and phrases: Voevodsky motive, dimension filtration, slice filtration, weight structure, triangulated category, Chow motive. Article available at http://dx.doi.org/10.4310/HHA.2018.v20.n1.a16 Copyright ⃝c 2018, International Press. Permission to copy for private use granted.",

year = "2018",

doi = "10.4310/HHA.2018.v20.n1.a16",

language = "English",

volume = "20",

pages = "259--274",

journal = "Homology, Homotopy and Applications",

issn = "1532-0073",

publisher = "International Press of Boston, Inc.",

number = "1",

}

RIS

TY - JOUR

T1 - Intersecting the dimension and slice filtrations for motives

AU - Бондарко, Михаил Владимирович

N1 - Funding Information: Research is supported by the Russian Science Foundation grant No. 16-11-10200. Received June 16, 2017, revised November 13, 2017; published on February 21, 2018. 2010 Mathematics Subject Classification: Primary: 14C15, 18E30. Secondary: 19E15, 14C25, 18E35. Key words and phrases: Voevodsky motive, dimension filtration, slice filtration, weight structure, triangulated category, Chow motive. Article available at http://dx.doi.org/10.4310/HHA.2018.v20.n1.a16 Copyright ⃝c 2018, International Press. Permission to copy for private use granted.

PY - 2018

Y1 - 2018

N2 - In this note we prove that the intersections of the levels of the dimension filtration on Voevodsky's motivic complexes over a field with the levels of the slice filtration are "as small as possible". This statement is applied to prove that a conjecture of Ayoub is equivalent to a certain orthogonality assumption.

AB - In this note we prove that the intersections of the levels of the dimension filtration on Voevodsky's motivic complexes over a field with the levels of the slice filtration are "as small as possible". This statement is applied to prove that a conjecture of Ayoub is equivalent to a certain orthogonality assumption.

KW - Chow motive

KW - Dimension filtration

KW - Slice filtration

KW - Triangulated category

KW - Voevodsky motive

KW - Weight structure

UR - http://www.scopus.com/inward/record.url?scp=85042557147&partnerID=8YFLogxK

U2 - 10.4310/HHA.2018.v20.n1.a16

DO - 10.4310/HHA.2018.v20.n1.a16

M3 - Article

VL - 20

SP - 259

EP - 274

JO - Homology, Homotopy and Applications

JF - Homology, Homotopy and Applications

SN - 1532-0073

IS - 1

ER -

ID: 15489556