Navegar

Colección

Datos Estadísticas

Parte de libro

Cortiñas, G.; Haesemeyer, C.; Walker, M.E.; Weibel, C.A. "The k-theory of toric schemes over regular rings of mixed characteristic" (2018) Singularities, Algebraic Geometry, Commutative Algebra, and Related Topics: Festschrift for Antonio Campillo on the Occasion of his 65th Birthday:455-479
Estamos trabajando para incorporar este artículo al repositorio
Consulte el artículo en la página del editor

Abstract:

We show that if X is a toric scheme over a regular commutative ring k then the direct limit of the K-groups of X taken over any infinite sequence of nontrivial dilations is homotopy invariant. This theorem was previously known for regular commutative rings containing a field. The affine case of our result was conjectured by Gubeladze. We prove analogous results when k is replaced by an appropriate K-regular, not necessarily commutative k-algebra. © Springer Nature Switzerland AG 2018. All Rights Reserved.

Registro:

Documento: Parte de libro
Título:The k-theory of toric schemes over regular rings of mixed characteristic
Autor:Cortiñas, G.; Haesemeyer, C.; Walker, M.E.; Weibel, C.A.
Filiación:Department of Matemática-Inst. Santaló, FCEyN, Universidad de Buenos Aires, Buenos Aires, Argentina
School of Mathematics and Statistics, University of Melbourne, Melbourne, VIC, Australia
Department of Mathematics, University of Nebraska - Lincoln, Lincoln, NE, United States
Department of Mathematics, Rutgers University, New Brunswick, NJ, United States
Año:2018
Página de inicio:455
Página de fin:479
DOI: http://dx.doi.org/10.1007/978-3-319-96827-8_19
Título revista:Singularities, Algebraic Geometry, Commutative Algebra, and Related Topics: Festschrift for Antonio Campillo on the Occasion of his 65th Birthday
Título revista abreviado:Singul., Algebr. Geom., Commut. Algebr., and Relat. Top.: Festschr. for Antonio Campillo on the Occas. of his 65th Birthd.
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_97833199_v_n_p455_Cortinas

Referencias:

  • Bierstone, E., Milman, P., Desingularization of toric and binomial varieties (2006) J. Alg. Geom, 15, pp. 443-486
  • Blumberg, A., Mandell, M., Localization theorems in topological Hochschild homology and topological cyclic homology (2012) Geom. Topol, 16, pp. 1053-1120
  • Cisinski, D.-C., Tabuada, G., Symmetric monoidal structure on non-commutative motives (2012) J. K-Theory, 9 (2), pp. 201-268
  • Cortiñas, G., The obstruction to excision in K-theory and cyclic homology (2006) Invent. Math, 164, pp. 143-173
  • Cortiñas, G., Thom, A., Algebraic geometry of topological spaces I (2012) Acta Math, 209, pp. 83-131
  • Cortiñas, G., Rodríguez Cirone, E., Singular coefficients in the K-theoretic Farrell-Jones conjecture (2016) Algebr. Geom. Topol, 16, pp. 129-147
  • Cortiñas, G., Haesemeyer, C., Schlichting, M., Weibel, C., Cyclic homology, cdh-cohomology and negative K-theory (2008) Ann. Math, 167, pp. 549-563
  • Cortiñas, G., Haesemeyer, C., Walker, M., Weibel, C., The K-theory of toric varieties (2009) Trans. AMS, 361, pp. 3325-3341
  • Cortiñas, G., Haesemeyer, C., Walker, M., Weibel, C., TheK-theory of toric varieties in positive characteristic (2014) J. Topol, 7, pp. 247-286
  • Cortiñas, G., Haesemeyer, C., Walker, M., Weibel, C., Toric varieties, monoid schemes and cdh descent (2015) J. Reine Angew. Math, 698, pp. 1-54
  • Geisser, T., Hesselholt, L., On the K-theory and topological cyclic homology of smooth schemes over a discrete valuation ring (2006) Trans. AMS, 358, pp. 131-145
  • 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
  • Goodwillie, T., Cyclic homology, derivations, and the free loopspace (1985) Topology, 24, pp. 187-215
  • Goodwillie, T., Relative algebraic K-theory and cyclic homology (1986) Ann. Math, 124, pp. 347-402
  • Grothendieck, A., élements de Géométrie Algébrique, III (1961) étude cohomologique des faisceaux cohérents (première partie), 11, p. 167. , IHES, Paris Publications Mathématiques
  • Gubeladze, J., Geometric and algebraic representations of commutative cancellative monoids (1995) Proc. A. Razmadze Math. Inst, 113, pp. 31-81
  • Gubeladze, J., Higher K-theory of toric varieties (2003) K-Theory, 28, pp. 285-327
  • Gubeladze, J., The nilpotence conjecture in K-theory of toric varieties (2005) Inventiones Math, 160, pp. 173-216
  • Gubeladze, J., Global coefficient ring in the nilpotence conjecture (2008) Trans. AMS, 136, pp. 499-503
  • Hesselholt, L., Madsen, I., On the K-theory of finite algebras overWitt vectors of perfect fields (1997) Topology, 36, pp. 29-101
  • Hochster, M., Rings of invariants of tori, Cohen-Macaulay rings generated by monomials, and polytopes (1972) Ann. Math, 96, 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
  • Keller, B., On differential graded categories (2006) In: Proceedings of Barcelona ICM, 2, pp. 151-190. , European Mathematical Society, Zürich
  • McCarthy, R., The cyclic homology of an exact category (1994) J. Pure Appl. Algebra, 93 (3), pp. 251-296
  • McCarthy, R., Relative algebraic K-theory and topological cyclic homology (1997) Acta Math, 179, pp. 197-222
  • Rodríguez Cirone, E., (2015) A strictly-functorial and small dg-enhancement of the derived category of perfect complexes, , Preprint
  • Swan, R.G., Projective modules over Laurent polynomial rings (1978) Trans. AMS, 237, pp. 111-120
  • Swan, R.G., Néron-Popescu desingularizatio (1998) In: Algebra and Geometry, 2, pp. 135-192. , International Press, Cambridge (Taipei, 1995). Lectures on Algebraic Geometry
  • Tabuada, G., En-regularity implies En-1-regularity (2014) Documenta Math, 19, pp. 121-139
  • Thomason, R.W., Trobaugh, T., Higher algebraic K-theory of schemes and of derived categories In: The Grothendieck Festschrift, vol. III (1990) Progress in Mathematics, 88, pp. 247-435. , Birkhäuser, Boston
  • van der Kallen, W., Descent for the K-theory of polynomial rings (1986) Math. Z, 191 (3), pp. 405-415
  • Voevodsky, V., Homotopy theory of simplicial sheaves in completely decomposable topologies (2010) J. Pure Appl. Algebra, 214, pp. 1384-1398
  • Weibel, C.A., Homotopy algebraic K-theor (1989) In: Algebraic K-Theory and Algebraic Number Theory, 83, pp. 461-488. , AMS, Providence (Honolulu 1987). Contemporary Mathematics
  • Weibel, C.A., (1994) An Introduction to Homological Algebra, , Cambridge University Press, Cambridge
  • Weibel, C.A., The K-Boook. An Introduction to Algebraic K-Theory (2013) Graduate Studies in Mathematics, 145. , AMS, Providence

Citas:

---------- APA ----------
Cortiñas, G., Haesemeyer, C., Walker, M.E. & Weibel, C.A. (2018) . The k-theory of toric schemes over regular rings of mixed characteristic. Singularities, Algebraic Geometry, Commutative Algebra, and Related Topics: Festschrift for Antonio Campillo on the Occasion of his 65th Birthday, 455-479.
http://dx.doi.org/10.1007/978-3-319-96827-8_19
---------- CHICAGO ----------
Cortiñas, G., Haesemeyer, C., Walker, M.E., Weibel, C.A. "The k-theory of toric schemes over regular rings of mixed characteristic" . Singularities, Algebraic Geometry, Commutative Algebra, and Related Topics: Festschrift for Antonio Campillo on the Occasion of his 65th Birthday (2018) : 455-479.
http://dx.doi.org/10.1007/978-3-319-96827-8_19
---------- MLA ----------
Cortiñas, G., Haesemeyer, C., Walker, M.E., Weibel, C.A. "The k-theory of toric schemes over regular rings of mixed characteristic" . Singularities, Algebraic Geometry, Commutative Algebra, and Related Topics: Festschrift for Antonio Campillo on the Occasion of his 65th Birthday, 2018, pp. 455-479.
http://dx.doi.org/10.1007/978-3-319-96827-8_19
---------- VANCOUVER ----------
Cortiñas, G., Haesemeyer, C., Walker, M.E., Weibel, C.A. The k-theory of toric schemes over regular rings of mixed characteristic. Singul., Algebr. Geom., Commut. Algebr., and Relat. Top.: Festschr. for Antonio Campillo on the Occas. of his 65th Birthd. 2018:455-479.
http://dx.doi.org/10.1007/978-3-319-96827-8_19