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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2013
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| Acceso en línea: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_10563911_v22_n1_p13_Cortinas http://hdl.handle.net/20.500.12110/paper_10563911_v22_n1_p13_Cortinas |
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| Sumario: | 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. |
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