show · g2c.good_reduction all knowls · up · search:

A variety $X$ over $\mathbb{Q}$ is said to have good reduction at a prime $p$ if it has an integral model whose reduction modulo $p$ defines a smooth variety of the same dimension; otherwise, $p$ 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 $g>1$.

Knowl status:
  • Review status: reviewed
  • Last edited by John Cremona on 2018-05-24 16:48:18
Referred to by:
History: (expand/hide all)