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Results tagged with field-with-one-element
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user 914
This tag refers to the (non-existent) "field of one element".
63
votes
Accepted
What is the field with one element?
As other have mentioned, F_1 does not exist of a field. Tits conjectured the existence of a "field of characteristic one" F_1 for which one would have the equality G(F_1) = W, where G is any Chevalley …
- 2,941
4
votes
Elliptic Curves over F_1?
In most of the current schemes, it is very unlikely that elliptic curves are defined over F_1.
They are certainly not in Deitmar's or Toen-Vaquie since they restric to toric varieties. For Soule/Conne …
- 2,941
3
votes
Accepted
What should Spec Z[\sqrt{D}] x_{F_1} Spec \bar{F_1} be?
Sorry I didn't reply before, I somehow didn't read the question till now.
I think your question is a bit misguided. The main problem I see with it is: what is $\text{Spec} \mathbb{Z}[\sqrt{D}]$ over F …
- 2,941
3
votes
Are the closures of the tori in the decomposition of a torified variety toric varieties?
Sorry that I reply so late, I haven't been hanging much on MO recently.
The quick answer to your question is no, the closure of tori appearing in the torification are in general not toric varieties. …
- 2,941