Definition 42.2.2 (02PH)—The Stacks project

Loading web-font TeX/Main/Regular

Table of contents
Part 3: Topics in Scheme Theory
Chapter 42: Chow Homology and Chern Classes
Section 42.2: Periodic complexes and Herbrand quotients
Definition 42.2.2 (cite)

numberstags

Definition 42.2.2. Let $(M, N, \varphi , \psi )$ be a $2$ -periodic complex over a ring $R$ whose cohomology modules have finite length. In this case we define the multiplicity of $(M, N, \varphi , \psi )$ to be the integer

$e_ R(M, N, \varphi , \psi ) = \text{length}_ R(H^0(M, N, \varphi , \psi )) - \text{length}_ R(H^1(M, N, \varphi , \psi ))$

In the case of a $(2, 1)$ -periodic complex $(M, \varphi , \psi )$ , we denote this by $e_ R(M, \varphi , \psi )$ and we will sometimes call this the (additive) Herbrand quotient.

Comments (0)

There are also:

2 comment(s) on Section 42.2: Periodic complexes and Herbrand quotients

In your comment you can use Markdown and LaTeX style mathematics (enclose it like $\pi$ ). A preview option is available if you wish to see how it works out (just click on the eye in the toolbar).

Comments (0)

Post a comment