Intersection theory of algebraic obstructions

[摘要] Let A be a noetherian commutative ring of dimension d and L be a rank one projective A-module. For 1 <= r <= d, we define obstruction groups E-r (A, L). This extends the original definition due to Nori, in the case r = d. These groups would be called Euler class groups. In analogy to intersection theory in algebraic geometry, we define a product (intersection) E-r (A, A) x E-s (A, A) -> Er+s (A, A). For a projective A-module Q of rank n <= d, with an orientation chi : L (->) over tilde Lambda(n) Q, we define a Chern class like homomorphism omega(Q, chi) : Ed-n (A, L') -> E-d (A, LL'), where L' is another rank one projective A-module. (c) 2010 Elsevier B.V. All rights reserved.

[发布日期] 2010-12-01