Revision as of 15:32, 23 January 2008 by imported>David E. Volk
Definition
Let
be a commutative ring. A formal group in one parameter is a series
such that
![{\displaystyle F(X,0)=F(0,X)=X}](https://wikimedia.org/api/rest_v1/media/math/render/svg/380a4cbf6e88a60dd48b5d2042281d2f0a92255d)
![{\displaystyle F(X,Y)=F(Y,X)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/395ddd11992f20751a544bd522cf53b57e210b4a)
in ![{\displaystyle A[[X,Y,Z]]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/826428ffe80a3500e6a6878678d46f4be473f6d0)
- There is a series
such that ![{\displaystyle F(X,\sigma (X))=0}](https://wikimedia.org/api/rest_v1/media/math/render/svg/52c1e094ef1c0accc63c9a11855f69981799b8e0)
Examples
- The additive formal group:
![{\displaystyle F(X,Y)=X+Y}](https://wikimedia.org/api/rest_v1/media/math/render/svg/8a0baa24075e3c313e7ba989059e090782374c61)
- The multiplicative formal group:
. In this case,
.