Timeline for Intrinsic topology on the Zariski spectrum
Current License: CC BY-SA 4.0
3 events
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| Mar 2, 2023 at 13:42 | comment | added | Peter Scholze | The value of that thing at $X$ wouldn't be the spectrum of the ring at $X$; rather, the spectrum is some kind of total space over $\mathcal C$ and the value at $X$ are sections of it. These have the correct variance. | |
| Mar 2, 2023 at 10:06 | comment | added | Zhen Lin | Is it really that simple? Maybe I missed a step. Fix a site $\mathcal{C}$. Suppose there were a general construction turning sheaves $\mathcal{C}^\textrm{op} \to \textbf{CRing}$ into sheaves $\mathcal{C}^\textrm{op} \to \textbf{Set}$ such that the value at $X$ is the prime spectrum of the ring at $X$, at least for some selected $X$. Then in particular we could do this for $\mathcal{C} = \textbf{CRing}^\textrm{op}$ and the identity functor to get a covariant (!) functor $\textbf{CRing} \to \textbf{Set}$ whose value at some selected $X$ is the prime spectrum of $X$... | |
| Mar 1, 2023 at 13:09 | history | answered | Peter Scholze | CC BY-SA 4.0 |