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Results tagged with schemes
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user 111491
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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Field extensions in Grothendieck rings
Indeed, by the Larsen-Lunts theorem for smooth projective connected schemes of finite type $[X] = [Y]$ implies that $X$ and $Y$ are stably birational; this applies to $\mathrm{Spec}(K)$, $\mathrm{Spec} … Same argument applies to products of fields that is to reduced zero-dimensional finite $k$-schemes: here the Larsen-Lunts theorem will match up the stable birational types of the connected components. …
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