 Solution

ID: past-exam-of-the-introduction-to-schemes-course-of-the-university-of-oxford/2023/1/a/ii/solution

T

(j_{i} : U_{i} ↪ T)_{i \in I}

whose images cover its underlying topological space:

T = i \in I ⋃ j_{i} (U_{i}) .

There is no finiteness requirement. Intersections used in the sheaf on a site condition are the pullbacks

U_{i} \times_{T} U_{j}

, identified with the corresponding open subschemes

U_{i} \cap U_{j}

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