Timeline for A path between two maximal ideals of a commutative ring
Current License: CC BY-SA 4.0
4 events
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| Dec 20, 2020 at 2:38 | history | edited | LSpice | CC BY-SA 4.0 |
\DeclareMathOperator
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| Dec 20, 2020 at 1:25 | comment | added | Antoine Labelle | More generally, if we consider the graph whose vertices are the irreducible components and two components are connected by an edge iff they intersect, then two points of the spectrum are path connected iff their irreducible components are in the same connected component of the graph. | |
| Dec 19, 2020 at 20:52 | comment | added | Antoine Labelle | As we can pass through the generic point, there exist a path between any two closed points of the same irreducible component. Moreover if two irreducible component share a point we can use it to pass from one to the other. Hence, at least if the number of irreducible components is finite (for example if R is noetherian), such a path exist iff the two closed points are in the same connected component. | |
| Dec 19, 2020 at 19:43 | history | asked | Biller Alberto | CC BY-SA 4.0 |