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Matematicheskie Zametki, 2010, Volume 87, Issue 3, Pages 369–381
DOI: https://doi.org/10.4213/mzm4117 (Mi mzm4117) 		 
This article is cited in 4 scientific papers (total in 4 papers)

Zeta Functions in Triangulated Categories

V. I. Guletskii

University of Liverpool
Full-text PDF (523 kB) Citations (4)
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DOI: https://doi.org/10.4213/mzm4117
Abstract: We prove the 2-out-of-3 property for the rationality of motivic zeta function in distinguished triangles in Voevodsky's category DM. As an application, we show the rationality of motivic zeta functions for all varieties whose motives are in the thick triangulated monoidal subcategory generated by motives of quasi-projective curves in DM. Together with a result due to P. O'Sullivan, this also gives an example of a variety whose motive is not finite-dimensional while the motivic zeta function is rational.
Keywords: zeta function, motivic measure, finite-dimensional motives, triangulated category of motives over a field, homotopy category of motivic symmetric spectra, Grothendieck group of a triangulated category, λ-ring, rationality.
Received: 04.10.2007
Revised: 17.09.2009
English version:
Mathematical Notes, 2010, Volume 87, Issue 3, Pages 345–354
DOI: https://doi.org/10.1134/S0001434610030053
Bibliographic databases:
Document Type: Article
UDC: 513.6
Language: Russian
Citation: V. I. Guletskii, “Zeta Functions in Triangulated Categories”, Mat. Zametki, 87:3 (2010), 369–381; Math. Notes, 87:3 (2010), 345–354
Citation in format AMSBIB
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\paper Zeta Functions in Triangulated Categories
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\vol 87
\issue 3
\pages 369--381
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  • https://doi.org/10.4213/mzm4117
  • https://www.mathnet.ru/eng/mzm/v87/i3/p369
    • This publication is cited in the following 4 articles:
    1. Gorchinskiy S., Guletskii V., “Symmetric powers in abstract homotopy categories”, Adv. Math., 292 (2016), 707–754  crossref  mathscinet  zmath  isi  elib  scopus
    2. Ramachandran N., Tabuada G., “Exponentiable Motivic Measures”, J. Ramanujan Math. Soc., 30:4 (2015), 349–360  mathscinet  isi  elib
    3. Mazza C., Weibel C., “Schur-Finiteness in Lambda-Rings”, J. Algebra, 374 (2013), 66–78  crossref  mathscinet  zmath  isi  elib  scopus
    4. Biglari Sh., “On Lambda Operations on Mixed Motives”, J. K-Theory, 12:2 (2013), 381–404  crossref  mathscinet  zmath  isi  scopus
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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