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Results tagged with schemes
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user 38432
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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Can I conclude that a morphism of vector bundles is zero if it is so fiberwise?
Let $f: X \rightarrow Y$ be a flat morphism of locally noetherian schemes and $\varphi: \mathcal U \rightarrow \mathcal V$ a map of vector bundles (locally free sheaves of finite rank) on $X$. … If not, are there additional assumptions on the schemes or on $f$ that would imply the vanishing of $\varphi$ ?
Note that I do not want to assume that the cokernel of $\varphi$ is locally free. …
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