$K_{1}$ 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
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
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 ${K_1}(A)$.
- Hyman Bass, Algebraic $K$-theory, W. A. Benjamin, Inc., New York-Amsterdam, 1968. MR 0249491 A. Grothendieck, Élements de géométrie algébrique. II. Étude globale élémentaire de quelques classes de morphismes, Inst. Hautes Études Sci. Publ. Math. No. 8 (1961). MR 36 #l77b. SGA 6 (1966-67) Théorie globale des intersections et Théorème de Riemann-Roch, Inst. Hautes Études Sci.
- Leslie G. Roberts, $K_{1}$ of some abelian categories, Trans. Amer. Math. Soc. 138 (1969), 377–382. MR 251109, DOI https://doi.org/10.1090/S0002-9947-1969-0251109-4
Retrieve articles in Proceedings of the American Mathematical Society with MSC: 14.55
Retrieve articles in all journals with MSC: 14.55
Additional Information
Keywords:
<IMG WIDTH="32" HEIGHT="38" ALIGN="MIDDLE" BORDER="0" SRC="images/img2.gif" ALT="${K_1}$">,
locally free sheaf,
projective <IMG WIDTH="15" HEIGHT="20" ALIGN="BOTTOM" BORDER="0" SRC="images/img1.gif" ALT="$r$">-space
Article copyright:
© Copyright 1970
American Mathematical Society