This paper contains the algebraic analog for idempotent matrices of the Chern-Weil theory of characteristic classes. This is used to show, algebraically, that the canonical line bundle on the complex projective space is not stably trivial. Also a theorem is proved saying that for any smooth manifold there is a canonical epimorphism from the even dimensional algebraic de Rham cohomology of its algebra of smooth functions onto the standard even dimensional de Rham cohomology of the manifold.
@article{urn:eudml:doc:41737,
title = {Algebraic characteristic classes for idempotent matrices.},
journal = {Publicacions Matem\`atiques},
volume = {36},
year = {1992},
pages = {601-608},
mrnumber = {MR1209826},
zbl = {0771.55007},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:41737}
}
Gómez, Francisco. Algebraic characteristic classes for idempotent matrices.. Publicacions Matemàtiques, Tome 36 (1992) pp. 601-608. http://gdmltest.u-ga.fr/item/urn:eudml:doc:41737/