Artículo

Cortiñas, G.; Haesemeyer, C.; Walker, M.E.; Weibel, C. "Toric varieties, monoid schemes and cdh descent" (2015) Journal fur die Reine und Angewandte Mathematik(698):1-54
Estamos trabajando para incorporar este artículo al repositorio
Consulte el artículo en la página del editor
Consulte la política de Acceso Abierto del editor

Abstract:

We give conditions for the Mayer-Vietoris property to hold for the algebraic K-theory of blow-up squares of toric varieties and schemes, using the theory of monoid schemes. These conditions are used to relate algebraic K-theory to topological cyclic homology in characteristic p. To achieve our goals, we develop many notions for monoid schemes based on classical algebraic geometry, such as separated and proper maps and resolution of singularities. © De Gruyter 2015.

Registro:

Documento: Artículo
Título:Toric varieties, monoid schemes and cdh descent
Autor:Cortiñas, G.; Haesemeyer, C.; Walker, M.E.; Weibel, C.
Filiación:Departamento Matemática-Instituto Santaló, Universidad de Buenos Aires, Ciudad Universitaria, Buenos Aires, 1428, Argentina
Department of Mathematics, University of California, 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:2015
Número:698
Página de inicio:1
Página de fin:54
DOI: http://dx.doi.org/10.1515/crelle-2012-0123
Título revista:Journal fur die Reine und Angewandte Mathematik
Título revista abreviado:J. Reine Angew. Math.
ISSN:00754102
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00754102_v_n698_p1_Cortinas

Referencias:

  • Bierstone, E., Milman, P., Desingularization of toric and binomial varieties (2006) J. Algebraic Geom., 15, pp. 443-486
  • Blander, B.A., Local projective model structures on simplicial presheaves (2001) K-Theory, 24, pp. 283-301
  • Bousfield, A.K., Friedlander, E.M., Homotopy theory of Γ-spaces, spectra, and bisimplicial sets (1978) Lecture Notes in Math., 658, pp. 80-130. , Geometric applications of homotopy theory. II (Evanston 1977), Springer-Verlag, Berlin
  • Connes, A., Consani, C., Schemes over F1 and zeta functions (2010) Compos. Math., 146, pp. 1383-1415
  • Connes, A., Consani, C., On the notion of geometry over F1 (2011) J. Algebraic Geom., 20, pp. 525-557
  • Connes, A., Consani, C., Marcolli, M., Fun with F1 (2009) J. Number Theory, 129, pp. 1532-1561
  • Cortiñas, G., Haesemeyer, C., Schlichting, M., Weibel, C., Cyclic homology, cdh-cohomology and negative K-theory (2008) Ann. Of Math., 167 (2), pp. 549-573
  • Deitmar, A., F1-schemes and toric varieties (2008) Beitr. Algebra Geom., 49, pp. 517-525
  • Eisenbud, D., Harris, J., The geometry of schemes (2000) Grad. Texts in Math., 197. , Springer-Verlag, New York
  • Fulton, W., Introduction to toric varieties (1993) Ann. Of Math. Stud., 131. , Princeton University Press, Princeton
  • Geisser, T., Hesselholt, L., Bi-relative algebraic K-theory and topological cyclic homology (2006) Invent. Math., 166, pp. 359-395
  • Geisser, T., Hesselholt, L., On the vanishing of negative K-groups (2010) Math. Ann., 348, pp. 707-736
  • Geisser, T., Hesselholt, L., On relative and bi-relative algebraic K-theory of rings of finite characteristic (2011) J. Amer. Math. Soc., 24, pp. 29-49
  • Gilmer, R., (1984) Commutative Semigroup Rings, , The University of Chicago Press, Chicago
  • Grothendieck, A., Élements de géométrie algébrique. II: Étude globale élémentaire de quelques classe de morphismes (1961) Publ. Math. Inst. Hautes Études Sci., 8, pp. 1-222
  • Grothendieck, A., Élements de géométrie algébrique. IV: Étude locale des schemas et des morphismes de schemas (2eme partie) (1964) Publ. Math. Inst. Hautes Études Sci., 24, pp. 1-231
  • Grothendieck, A., Dieudonné, J., Élements de géométrie algébrique. I (1971) Grundlehren Math. Wiss., p. 166. , Springer-Verlag, Berlin
  • Gubeladze, J., K-theory of affine toric varieties (1999) Homology, Homotopy Appl., 1, pp. 135-145
  • Haesemeyer, C., Descent properties of homotopy K-theory (2004) Duke Math. J., 125, pp. 589-620
  • Hartshorne, R., Algebraic geometry (1977) Grad. Texts in Math., 52. , Springer-Verlag, New York
  • Hattori, A., Theory of multi-fans (2003) Osaka J. Math., 40, pp. 1-68
  • Hochster, M., Rings of invariants of tori, Cohen - Macaulay rings generated by monomials, and polytopes (1972) Ann. Of Math., 96 (2), pp. 318-337
  • Jardine, J.F., Simplicial presheaves (1987) J. Pure Appl. Algebra, 47, pp. 35-87
  • Jardine, J.F., (1997) Generalized Étale Cohomology Theories, , Birkhäuser-Verlag, Basel
  • Kato, K., Toric singularities (1994) Amer. J. Math., 116, pp. 1073-1099
  • López Peña, J., Lorscheid, O., Mapping F1-land: An overview of geometries over the field with one element (2011) Noncommutative Geometry, Arithmetic, and Related Topics (Baltimore 2009), pp. 241-265. , Johns Hopkins University Press, Baltimore
  • Popescu, D., General Néron desingularization and approximation (1986) Nagoya Math. J., 104, pp. 85-115
  • Thomason, R.W., Les K-groupes d'un schéma éclaté et une formule d'intersection excédentaire (1993) Invent. Math., 112, pp. 195-215
  • Thomason, R.W., Trobaugh, T., Higher algebraic K-theory of schemes and of derived categories (1990) Progr. Math., 88, pp. 247-436. , The Grothendieck Festschrift, vol. III, Birkhäuser-Verlag, Boston
  • Voevodsky, V., Homotopy theory of simplicial sheaves in completely decomposable topologies (2010) J. Pure Appl. Algebra, 214, pp. 1384-1398
  • Voevodsky, V., Unstable motivic homotopy categories in Nisnevich and cdh-topologies (2010) J. Pure Appl. Algebra, 214, pp. 1399-1406
  • Weibel, C., Homotopy algebraic K-theory (1989) Contemp. Math., 83, pp. 461-488. , Algebraic K-theory and algebraic number theory (Honolulu 1987), American Mathematical Society, Providence
  • Weibel, C., The negative K-theory of normal surfaces (2001) Duke Math. J., 108, pp. 1-35
  • Zariski, O., Samuel, P., Commutative algebra, vol. II, reprint of the 1958-1960 Van Nostrand edition (1975) Grad. Texts in Math., 29. , Springer-Verlag, New York

Citas:

---------- APA ----------
Cortiñas, G., Haesemeyer, C., Walker, M.E. & Weibel, C. (2015) . Toric varieties, monoid schemes and cdh descent. Journal fur die Reine und Angewandte Mathematik(698), 1-54.
http://dx.doi.org/10.1515/crelle-2012-0123
---------- CHICAGO ----------
Cortiñas, G., Haesemeyer, C., Walker, M.E., Weibel, C. "Toric varieties, monoid schemes and cdh descent" . Journal fur die Reine und Angewandte Mathematik, no. 698 (2015) : 1-54.
http://dx.doi.org/10.1515/crelle-2012-0123
---------- MLA ----------
Cortiñas, G., Haesemeyer, C., Walker, M.E., Weibel, C. "Toric varieties, monoid schemes and cdh descent" . Journal fur die Reine und Angewandte Mathematik, no. 698, 2015, pp. 1-54.
http://dx.doi.org/10.1515/crelle-2012-0123
---------- VANCOUVER ----------
Cortiñas, G., Haesemeyer, C., Walker, M.E., Weibel, C. Toric varieties, monoid schemes and cdh descent. J. Reine Angew. Math. 2015(698):1-54.
http://dx.doi.org/10.1515/crelle-2012-0123