Several complex variables and analytic spaces Local analytic geometry Concept
Ring of convergent power series
Summary
The ring of convergent power series consists of the formal power series in variables that converge on some neighbourhood of the origin. It is a subring of the ring of multivariate formal power series . It is isomorphic to the ring of germs of holomorphic functions at , and it is the basic algebraic object of local analytic geometry. It is a Noetherian local unique factorization domain, as is its formal completion.
Where this leads
13 pages build on this one.
- Cartan's coherence theorem for ideal sheaves
- The local ring of holomorphic germs is Noetherian and factorial
- Weierstrass division theorem
- Milnor number
- Grauert's semicontinuity theorem
- Oka coherence theorem
- Mather–Yau theorem
- Complex analytic space
- Weierstrass polynomial
- Briançon–Skoda theorem
- Arnold's classification of simple singularities
- Grauert's direct image theorem
- Zariski's multiplicity conjecture
Further reading
About this page
| Tag | EVPZ7ZG1HB |
|---|---|
| URI | m2://EVPZ7ZG1HB |
| Kind | concept |
| Writing | W0 stub |
| MSC | 32B05, 13J07, 32A05 |
| Specializes | Multivariate formal power series |
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