Timeline for Can global fields be defined as certain topological fields like local fields?
Current License: CC BY-SA 4.0
8 events
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| Jun 1, 2023 at 20:59 | history | edited | Z Wu | CC BY-SA 4.0 |
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| Jun 1, 2023 at 20:57 | comment | added | Z Wu | @ChrisWuthrich You are right. What I really mean is that I want an axiomatic definition that doesn't use absolute values. I will edit the post. | |
| Jun 1, 2023 at 20:53 | comment | added | Z Wu | @WillSawin the axiomatic definition by Artin-Whaples, and the usual definition that list all the global fields. | |
| Jun 1, 2023 at 20:44 | comment | added | Will Sawin | What definition of global field are you familiar with? | |
| Jun 1, 2023 at 20:41 | comment | added | Chris Wuthrich | Global fields do not come with a preferred topology: I believe no definition of a global field will mention any absolute value. | |
| Jun 1, 2023 at 20:41 | comment | added | Z Wu | @WillSawin That sounds like a cool definition! Is there a reference using that definition or proving this equivalence? And is there a similar one for local fields? | |
| Jun 1, 2023 at 20:27 | comment | added | Will Sawin | Why not just define global fields as the fields of fractions of Dedekind domains of finite type over $\mathbb Z$? | |
| Jun 1, 2023 at 20:00 | history | asked | Z Wu | CC BY-SA 4.0 |