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.

See also

References

This article is issued from Wikipedia - version of the Saturday, November 29, 2014. The text is available under the Creative Commons Attribution/Share Alike but additional terms may apply for the media files.