IJPAM: Volume 52, No. 4 (2009)

ON THE K-THEORY OF VECTOR BUNDLES ON CURVES

E. Ballico
Department of Mathematics
University of Trento
380 50 Povo (Trento) - Via Sommarive, 14, ITALY
e-mail: ballico@science.unitn.it


Abstract.Let $X$ be a smooth genus $g \ge 2$ curve. Let $\mathcal {P}(X)$ be the exact category of vector bundles on $X$ $I \subset \mathbb {R}$ an interval and $\mathcal {P}(I)$ the exact subcategory generated by the bundles with slopes in $I$. Here we prove that the inclusion $\mathcal {P}(I) \to \mathcal {P}(X)$ induces isomorphisms of K-groups $K_i(\mathcal {P}(I)) \to K_i(\mathcal {P}(X))$ for all integers $i \ge 0$.

Received: February 24, 2009

AMS Subject Classification: 14H60

Key Words and Phrases: vector bundles on curves, K-theory of vector bundles on curves

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2009
Volume: 52
Issue: 4