Formal moduli
 | This article includes a list of references, related reading, or external links, but its sources remain unclear because it lacks inline citations. (February 2022) |
 | This article relies largely or entirely on a single source. (May 2024) |
In mathematics, formal moduli are an aspect of the theory of moduli spaces (of algebraic varieties or vector bundles, for example), closely linked to deformation theory and formal geometry. Roughly speaking, deformation theory can provide the Taylor polynomial level of information about deformations, while formal moduli theory can assemble consistent Taylor polynomials to make a formal power series theory. The step to moduli spaces, properly speaking, is an algebraization question, and has been largely put on a firm basis by Artin's approximation theorem.
A formal universal deformation is by definition a formal scheme over a complete local ring, with special fiber the scheme over a field being studied, and with a universal property amongst such set-ups. The local ring in question is then the carrier of the formal moduli.
References
- "Deformation", Encyclopedia of Mathematics, EMS Press, 2001 [1994]
 | This geometry-related article is a stub. You can help Wikipedia by adding missing information. |
 | This mathematical analysis–related article is a stub. You can help Wikipedia by adding missing information. |
Content Disclaimer
Informasi ini disarikan dari Wikipedia dan disajikan kembali untuk tujuan edukasi. Konten tersedia di bawah lisensi CC BY-SA 3.0. Kami tidak bertanggung jawab atas ketidakakuratan data yang bersumber dari kontribusi publik tersebut.
- The information displayed on this website is sourced in part or in whole from Wikipedia and has been adapted for the purpose of restating it. We strive to provide accurate and relevant information, however:
- There is no guarantee of absolute accuracy. Wikipedia is an open, collaborative project that can be edited by anyone, so information is subject to change.
- It is not intended to constitute professional advice. The content displayed is for informational and educational purposes only. For important decisions (e.g., medical, legal, or financial), please consult a professional.
- Content copyright. Wikipedia is licensed under the Creative Commons Attribution-ShareAlike License (CC BY-SA). This means that content may be reused with appropriate attribution and shared under a similar license.
- Responsible use. Any risk arising from the use of information from this website is entirely the responsibility of the user.