Vector Bundles on P1ℤ with Simple Jumps

Resumo

Vector bundles of rank 2 on the projective line over ℤ are considered. It is assumed that such a bundle E is trivial on a generic fiber, and its restriction to any special fiber is isomorphic either to O² or to O(−1)⊕O(1). Under these assumptions it is proved that an exact sequence of the form 0→O(−2) → E →O(2) → 0 exists.