Potential good reduction
In mathematics, potential good reduction is a property of the reduction modulo a prime or, more generally, prime ideal, of an algebraic variety.
Definitions
Good reduction refers to the reduced variety having the same properties as the original, for example, an algebraic curve having the same genus, or a smooth variety remaining smooth. Potential good reduction refers to the situation over a sufficiently large finite extension of the field of definition.
Equivalent formulations
For elliptic curves, potential good reduction is equivalent to the j-invariant being an algebraic integer.
gollark: I really need to work out how to type accented es.
gollark: Zombies are kind of cliched.
gollark: I mean, some people do need to work, and must also put their children somewhere.
gollark: It's one of the less bad approaches.
gollark: Apparently, yes.
See also
References
- Serre, Jean-Pierre; Tate, John (1968). "Good reduction of abelian varieties". The Annals of Mathematics. Second. 88 (3): 492–517. doi:10.2307/1970722. JSTOR 1970722. Zbl 0172.46101.
This article is issued from Wikipedia. The text is licensed under Creative Commons - Attribution - Sharealike. Additional terms may apply for the media files.