Consider and take the ideal
and the element
.
Consider reductions . Then
and
In particular, the bundle is semistable in the generic fiber, but not strongly semistable for any reduction
.
The corresponding torsor is an affine scheme for infinitely many prime reductions and not an affine scheme for infinitely many prime reductions.
![{\displaystyle {}\mathbb {Z} [x,y,z]/{\left(x^{7}+y^{7}+z^{7}\right)}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/4ee072447a0e22187b271df094af4971d1452df9)
![{\displaystyle f\in I^{*}{\text{ holds in }}\mathbb {Z} /(p)[x,y,z]/(x^{7}+y^{7}+z^{7}){\text{ for }}p\equiv 3\!\!\!\mod 7}](https://wikimedia.org/api/rest_v1/media/math/render/svg/5eb9fefbe5cf9bbc21f712e1db31a11fad9b34af)
![{\displaystyle f\not \in I^{*}{\text{ holds in }}\mathbb {Z} /(p)[x,y,z]/(x^{7}+y^{7}+z^{7}){\text{ for }}p\equiv 2\!\!\!\mod 7.}](https://wikimedia.org/api/rest_v1/media/math/render/svg/e4554166b04a1e2448f15cc37ef8e1f1570ce8ea)
