show · ag.good_reduction all knowls · up · search:

A variety $X$ over a number field $K$ is said to have good reduction at a prime $\mathfrak{p}$ if it has a model over $\mathcal{O}_{K, \mathfrak{p}}$ whose reduction modulo $\mathfrak{p}$ defines a smooth variety of the same dimension; otherwise, $\mathfrak{p}$ is said to be a prime of bad reduction.

When $X$ is a curve, any prime of good reduction for $X$ is also a prime of good reduction for its Jacobian, but the converse need not hold when $X$ has genus $g>1$.

Authors:
Knowl status:
  • Review status: beta
  • Last edited by Raymond van Bommel on 2020-08-25 08:09:47
Referred to by:
History: (expand/hide all)