Good and bad reduction: Difference between revisions

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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.

Further reading