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Results tagged with schemes
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user 2900
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.
2
votes
0
answers
281
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infinite dimensional germs of schemes and tangent spaces
(The question of the type "how to define?")
Let $(R,\mathfrak{m})$ be a local ring over a field $k$ of zero characteristic. Consider the matrices over this ring, $Mat(m,R)$. I think of $Mat(m,R)$ as …
- 2,232
4
votes
Components of an exceptional divisor
I'd say the number can be arbitrary large if $X$ is not assumed smooth along $Z$. Take the simplest example: hypersurface singularity $\{f_p+f_{p+1}=0\}\subset\Bbb C^n$, where $f_p$ is totally reducib …
- 2,232