K-theory of cones of smooth varieties

G. Cortiñas; C. Haesemeyer; M. E. Walker; C. Weibel

doi:10.1090/S1056-3911-2011-00583-3

K-theory of cones of smooth varieties

G. Cortiñas, C. Haesemeyer, M. E. Walker, C. Weibel

School of Arts and Sciences, Mathematics

Research output: Contribution to journal › Article › peer-review

9 Scopus citations

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.

Original language	English (US)
Pages (from-to)	13-34
Number of pages	22
Journal	Journal of Algebraic Geometry
Volume	22
Issue number	1
DOIs	https://doi.org/10.1090/S1056-3911-2011-00583-3
State	Published - 2013

All Science Journal Classification (ASJC) codes

Algebra and Number Theory
Geometry and Topology

Access to Document

10.1090/S1056-3911-2011-00583-3

Cite this

@article{eddd0a359cf04b3d94da84a83dd98789,

title = "K-theory of cones of smooth varieties",

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 K{\"a}hler differentials on the variety.",

author = "G. Corti{\~n}as and C. Haesemeyer and Walker, {M. E.} and C. Weibel",

year = "2013",

doi = "10.1090/S1056-3911-2011-00583-3",

language = "English (US)",

volume = "22",

pages = "13--34",

journal = "Journal of Algebraic Geometry",

issn = "1056-3911",

publisher = "American Mathematical Society",

number = "1",

}

TY - JOUR

T1 - K-theory of cones of smooth varieties

AU - Cortiñas, G.

AU - Haesemeyer, C.

AU - Walker, M. E.

AU - Weibel, C.

PY - 2013

Y1 - 2013

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84875191969&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84875191969&partnerID=8YFLogxK

U2 - 10.1090/S1056-3911-2011-00583-3

DO - 10.1090/S1056-3911-2011-00583-3

M3 - Article

AN - SCOPUS:84875191969

SN - 1056-3911

VL - 22

SP - 13

EP - 34

JO - Journal of Algebraic Geometry

JF - Journal of Algebraic Geometry

IS - 1

ER -

K-theory of cones of smooth varieties

Abstract

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Fingerprint

Cite this