K-theory of cones of smooth varieties
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(...
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todo:paper_10563911_v22_n1_p13_Cortinas2023-10-03T16:00:53Z K-theory of cones of smooth varieties Cortiñas, G. Haesemeyer, C. Walker, M.E. Weibel, C. 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. Fil:Cortiñas, G. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_10563911_v22_n1_p13_Cortinas |
| institution |
Universidad de Buenos Aires |
| institution_str |
I-28 |
| repository_str |
R-134 |
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) |
| description |
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. |
| format |
JOUR |
| author |
Cortiñas, G. Haesemeyer, C. Walker, M.E. Weibel, C. |
| spellingShingle |
Cortiñas, G. Haesemeyer, C. Walker, M.E. Weibel, C. K-theory of cones of smooth varieties |
| author_facet |
Cortiñas, G. Haesemeyer, C. Walker, M.E. Weibel, C. |
| author_sort |
Cortiñas, G. |
| title |
K-theory of cones of smooth varieties |
| title_short |
K-theory of cones of smooth varieties |
| title_full |
K-theory of cones of smooth varieties |
| title_fullStr |
K-theory of cones of smooth varieties |
| title_full_unstemmed |
K-theory of cones of smooth varieties |
| title_sort |
k-theory of cones of smooth varieties |
| url |
http://hdl.handle.net/20.500.12110/paper_10563911_v22_n1_p13_Cortinas |
| work_keys_str_mv |
AT cortinasg ktheoryofconesofsmoothvarieties AT haesemeyerc ktheoryofconesofsmoothvarieties AT walkerme ktheoryofconesofsmoothvarieties AT weibelc ktheoryofconesofsmoothvarieties |
| _version_ |
1782024028096036864 |