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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

$ K\sb{1}$ of projective $ r$-spaces


Author: Leslie G. Roberts
Journal: Proc. Amer. Math. Soc. 26 (1970), 587-592
MSC: Primary 14.55
DOI: https://doi.org/10.1090/S0002-9939-1970-0280501-0
MathSciNet review: 0280501
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Abstract: Let $ A$ be a commutative ring, and let $ X$ = projective $ r$-space over $ A$. Then we prove that $ {K_1}$ of the category of locally free sheaves of finite type on $ X$ is isomorphic to the direct sum of $ r + 1$ copies of $ {K_1}(A)$.


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DOI: https://doi.org/10.1090/S0002-9939-1970-0280501-0
Keywords: $ {K_1}$, locally free sheaf, projective $ r$-space
Article copyright: © Copyright 1970 American Mathematical Society