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Prime Ideals of Mixed Artin-Tate Motives

Published online by Cambridge University Press:  06 March 2013

Tobias J. Peter
Tobias J. Peter*
Affiliation:
Mathematics Department, UCLA, Los Angeles, CA 90095-1555, [email protected]
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Abstract

We show that for a field k, algebraic over ℚ, and F a field of characteristic zero, the triangular spectra of mixed Tate motives (resp. mixed Artin-Tate motives), denoted by DMT(k)F (resp. DMAT(k)F), are both isomorphic to spec(F). We further compute the Picard groups of DMT(k)F and DMAT(k)ℚ.

Keywords

mixed Artin-Tate motivestriangulated categoryPicard group14F4218E1018E30
Type
Research Article
Information
Journal of K-Theory , Volume 11 , Issue 2 , April 2013 , pp. 331 - 349
Copyright
Copyright © ISOPP 2013 

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References

1.André, Y., Une introduction aux motifs (motifs purs, motifs mixtes, périodes), Panoramas et Synthèses 17, Société Mathématique de France, Paris, 2004Google Scholar
2.Balmer, P., The spectrum of prime ideals in tensor triangulated categories, J. Reine Angew. Math. 588 (2005) 149–168CrossRefGoogle Scholar
3.Balmer, P., Spectra, spectra, spectra - tensor triangular spectra versus Zariski spectra of endomorphism rings, Algebr. Geom. Topol. 10 (3) (2010) 1521–1563CrossRefGoogle Scholar
4.Balmer, P., Tensor triangular geometry, In: Proceedings of the International Congress of Mathematicians (Hyderabad, 2010), II, 85–112, World Scientific Publishing Co., Hackensack, New Jersey, 2011Google Scholar
5.Beilinson, A. A., Bernstein, J. & Deligne, P., Faisceaux pervers, In: Analysis and topology on singular spaces, I (Luminy, 1981), Astérisque 100 (1982) 5–171, Soc. Math. France, ParisGoogle Scholar
6.Benson, D. J., Representations and cohomology I: Basic representation theory of finite groups and associative algebras, Cambridge Studies in Advanced Mathematics 30 (1998), Cambridge University Press, CambridgeGoogle Scholar
7.Biglari, S., A Künneth formula in tensor triangulated categories, J. Pure Appl. Algebra 210 (3) (2007) 645–650Google Scholar
8.Biglari, S., On finite dimensionality of mixed Tate motives, J. K-Theory 4 (1) (2009) 145–161Google Scholar
9.Borel, A., Stable real cohomology of arithmetic groups, Ann. Sci. École Norm. Sup. (4) 7 (1974, 1975) 235–272Google Scholar
10.Gabriel, P., Des catégories abéliennes, Bull. Soc. Math. France 90 (1962) 323–448Google Scholar
11.Levine, M., Tate motives and the vanishing conjectures for algebraic K-theory, In: Algebraic K-theory and algebraic topology (Lake Louise, AB, 1991), NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci. 407 (1993) 167–188, Kluwer Acad. Publ., DordrechtGoogle Scholar
12.Mazza, C., Voevodsky, V. & Weibel, C., Lecture notes on motivic cohomology, Clay Mathematics Monographs 2, American Mathematical Society, Providence, RI, 2006Google Scholar
13.Quillen, D., On the cohomology and K-theory of the general linear groups over a finite field, Ann. of Math. 96 (2) (1972) 552–586Google Scholar
14.Voevodsky, V., Triangulated categories of motives over a field, In: Cycles, transfers, and motivic homology theories, Ann. of Math. Stud. 143 (2000) 188–238, Princeton Univ. Press, Princeton, NJGoogle Scholar
15.Weibel, C. A., An introduction to homological algebra, Cambridge Studies in Advanced Mathematics 38, Cambridge University Press, Cambridge, 1994Google Scholar
16.Wildeshaus, J., Notes on Artin-Tate motives (2010), preprint: arXiv:0811.4551v2Google Scholar