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Results tagged with schemes
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user 99988
The first purpose of schemes theory is the geometrical study of solutions of algebraic systems of equations, not only over the real/complex numbers, but also over integer numbers (and more generally over any commutative ring with 1). It was finalized by Alexandre Grothendieck, during the 1950s and the 1960s.
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Are there nonaffine schemes over which every exact sequence of vector bundles is split?
Is there an example of a non-affine scheme $X$ such that every short exact sequence of vector bundles over $X$ splits? If there are such examples then what if we ask it to be true of all (not necessar …
- 187
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Are projective bundles corresponding to non-isomorphic vector bundles always non-isomorphic?
Is it always true that $\mathbb{P}(V)\cong \mathbb{P}(W)$ implies that $V\cong W$ as $S$-schemes?
If the statement is false then what is the most general condition on $S$ for which it becomes true? …
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