Good and bad reduction: Difference between revisions
From Elliptic Curve Crypto
create article |
No answers |
||
| Line 1: | Line 1: | ||
No answers on popular math sites? No explanatory or expository papers on the subject? Primary sources only? | |||
== Potential good reduction == | == Potential good reduction == | ||
:“For elliptic curves, potential good reduction is equivalent to the [[j-invariant]] being an algebraic integer” <ref>Wikipedia: Potential good reduction https://en.wikipedia.org/wiki/Potential_good_reduction</ref>. | :“For elliptic curves, potential good reduction is equivalent to the [[j-invariant]] being an algebraic integer” <ref>Wikipedia: Potential good reduction https://en.wikipedia.org/wiki/Potential_good_reduction</ref>. | ||
== Good reduction == | |||
:“Definition of ''good reduction'' (asked Mar 20, 2018 by 57Jimmy)” <ref>https://math.stackexchange.com/questions/2700158/definition-of-good-reduction</ref>. | |||
Good question, but no good answers as yet, six years later. | |||
== Bad reduction == | |||
:“bad reduction for elliptic curves (asked Feb 27, 2010 by schur)” <ref>https://mathoverflow.net/questions/16600/bad-reduction-for-elliptic-curves</ref>. | |||
A “nice try,” apparently. but still no good answers, 14 years later. | |||
* [https://www.lmfdb.org/knowledge/show/ec.bad_reduction Bad reduction of an elliptic curve at a prime (reviewed)] | |||
* [https://planetmath.org/BadReduction bad reduction] | |||
== Further reading == | |||
* [https://planetmath.org/minimalmodelforanellipticcurve minimal model for an elliptic curve] | |||
Latest revision as of 12:15, 8 January 2025
No answers on popular math sites? No explanatory or expository papers on the subject? Primary sources only?
Potential good reduction
- “For elliptic curves, potential good reduction is equivalent to the j-invariant being an algebraic integer” [1].
Good reduction
- “Definition of good reduction (asked Mar 20, 2018 by 57Jimmy)” [2].
Good question, but no good answers as yet, six years later.
Bad reduction
- “bad reduction for elliptic curves (asked Feb 27, 2010 by schur)” [3].
A “nice try,” apparently. but still no good answers, 14 years later.
