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Cortiñas, G.; Haesemeyer, C.; Walker, M.E.; Weibel, C. "K-theory of cones of smooth varieties" (2013) Journal of Algebraic Geometry. 22(1):13-34
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Abstract:

Let R be the homogeneous coordinate ring of a smooth projective variety X over a field k of characteristic 0. We calculate the κ-theory of R in terms of the geometry of the projective embedding of X. In particular, if X is a curve, then we calculate K0(R) and K1(R), and prove that K-1(R) = H1 (C, 0(n)). The formula for K0(R) involves the Zariski cohomology of twisted Kähler differentials on the variety.

Registro:

Documento: Artículo
Título:K-theory of cones of smooth varieties
Autor:Cortiñas, G.; Haesemeyer, C.; Walker, M.E.; Weibel, C.
Filiación:Departamento Matemática, FCEyN-UBA, Ciudad Universitaria Pab 1, 1428 Buenos Aires, Argentina
Department of Mathematics, UCLA, Los Angeles, CA 90095, United States
Department of Mathematics, University of Nebraska-Lincoln, Lincoln, NE 68588, United States
Department of Mathematics, Rutgers University, New Brunswick, NJ 08901, United States
Año:2013
Volumen:22
Número:1
Página de inicio:13
Página de fin:34
DOI: http://dx.doi.org/10.1090/S1056-3911-2011-00583-3
Título revista:Journal of Algebraic Geometry
Título revista abreviado:J. Algebraic Geom.
ISSN:10563911
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_10563911_v22_n1_p13_Cortinas

Referencias:

  • Cortiñas, G., Haesemeyer, C., Schlichting, M., Weibel, C., Cyclic homology, cdh-cohomology and negative K-theory (2008) Annals of Math., 167, pp. 549-563. , MR2415380 2009c:19006
  • Cortiñas, G., Haesemeyer, C., Weibel, C., K-regularity, cdh-fibrant Hochschild homology, and a conjecture of Vorst (2008) J. AMS, 21, pp. 547-561. , MR2373359 2008k:19002
  • Cortiñas, G., Haesemeyer, C., Weibel, C., Infinitesimal cohomology and the Chern character to negative cyclic homology (2009) Math. Ann., 344, pp. 891-922. , published electronically DOI: 10.1007/s00208-009-0333-9. MR2507630 2010i:19006
  • Cortiñas, G., Haesemeyer, C., Walker, M., Weibel, C., Bass' NK groups and cdhfibrant Hochschild homology (2010) Invent. Math., 181, pp. 421-448. , http://www.math.uiuc.edu/K-theory, MR2657430
  • Hartshorne, R., (1977) Algebraic Geometry, , Springer Verlag, MR0463157 57:3116
  • Geller, S., Reid, L., Weibel, C., Cyclic homology and K-theory of curves (1989) J. Reine Angew. Math., 393, pp. 39-90. , MR972360 89m:14006
  • Iitaka, S., (1982) Algebraic Geometry, Volume 76 of Graduate Texts in Mathematics, p. 24. , Springer-Verlag, New York, An introduction to birational geometry of algebraic varieties, North-Holland Mathematical Library, MR637060 84j:14001
  • Kassel, C., Cyclic homology, comodules, and mixed complexes (1987) J. Algebra., 107, pp. 195-216. , MR883882 88k:18019
  • Katz, N., Oda, T., On the differentiation of de Rham cohomology classes with respect to parameters (1968) J. Math. Kyoto Univ., 8 (2), pp. 199-213. , MR0237510 38:5792
  • Krishna, A., Srinivas, V., Zero-cycles and K-theory on normal surfaces (2002) Annals Math., 156, pp. 155-195. , MR1935844 2003k:14005
  • Krusemeyer, M., Fundamental groups, algebraic K-theory, and a problem of Abhyankar (1973) Invent. Math., 19, pp. 15-47. , MR0335522 49:303
  • Lewis, J., Saito, S., Algebraic cycles and Mumford-Griffiths invariants (2007) Amer. J. Math., 129, pp. 1449-1499. , MR2369886 2008j:14014
  • Michler, R., Hodge-components of cyclic homology for affine quasi-homogeneous hypersurfaces (1994) Astérisque, 226, pp. 321-333. , MR1317123 96a:19003
  • Murthy, M.P., Vector bundles over affine surfaces birationally equivalent to a ruled surface (1969) Annals of Math., 89, pp. 242-253. , MR0241434 39:2774
  • Soulé, C., Opérations en K-théorie algébrique (1985) Canad. J. Math., 37, pp. 488-550. , MR787114 87b:18013
  • Srinivas, V., Vector bundles on the cone over a curve (1982) Compositio Math., 47, pp. 249-269. , MR681609 84e:14017
  • Srinivas, V., Grothendieck groups of polynomial and Laurent polynomial rings (1986) Duke Math. J., 53, pp. 595-633. , MR860663 88a:14018
  • Srinivas, V., K1 of the cone over a curve (1987) J. Reine Angew. Math., 381, pp. 37-50. , MR918839 89e:14008
  • Swan, R.G., On seminormality (1980) J. Algebra., 67, pp. 210-229. , MR595029 82d:13006
  • Weibel, C., K2, K3 and nilpotent ideals (1980) J. Pure Appl. Alg., 18, pp. 333-345. , MR593622 82i:18016
  • Weibel, C., Mayer-vietoris sequences and module structures on NK* (1981) Lecture Notes in Math., 854, pp. 466-493. , Springer-Verlag, MR618317 82k:18010
  • Weibel, C., Homotopy algebraic k-theory (1989) AMS Contemp. Math., 83, pp. 461-488. , AMS, MR991991 90d:18006
  • Weibel, C., (1994) An Introduction to Homological Algebra, , Cambridge Univ. Press, MR1269324 95f:18001
  • Weibel, C., The negative K-theory of normal surfaces (2001) Duke Mathematical Journal, 108 (1), pp. 1-35. , DOI 10.1215/S0012-7094-01-10811-9
  • Zariski, O., Samuel, P., (1960) Commutative Algebra, 2. , University Series in Higher Mathematics. D. Van Nostrand Co., Inc., Princeton, N. J.-Toronto-London-New York, MR0120249 22:11006

Citas:

---------- APA ----------
Cortiñas, G., Haesemeyer, C., Walker, M.E. & Weibel, C. (2013) . K-theory of cones of smooth varieties. Journal of Algebraic Geometry, 22(1), 13-34.
http://dx.doi.org/10.1090/S1056-3911-2011-00583-3
---------- CHICAGO ----------
Cortiñas, G., Haesemeyer, C., Walker, M.E., Weibel, C. "K-theory of cones of smooth varieties" . Journal of Algebraic Geometry 22, no. 1 (2013) : 13-34.
http://dx.doi.org/10.1090/S1056-3911-2011-00583-3
---------- MLA ----------
Cortiñas, G., Haesemeyer, C., Walker, M.E., Weibel, C. "K-theory of cones of smooth varieties" . Journal of Algebraic Geometry, vol. 22, no. 1, 2013, pp. 13-34.
http://dx.doi.org/10.1090/S1056-3911-2011-00583-3
---------- VANCOUVER ----------
Cortiñas, G., Haesemeyer, C., Walker, M.E., Weibel, C. K-theory of cones of smooth varieties. J. Algebraic Geom. 2013;22(1):13-34.
http://dx.doi.org/10.1090/S1056-3911-2011-00583-3