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Diophantine equations, rational points, abelian varieties, Arakelov theory, Iwasawa theory.
4
votes
Questions about analogy between Spec Z and 3-manifolds
I cannot really say anything about relations with Poincare conjecture, but the obvious references you should look at are
M. Morishita. On certain analogies between knots and primes. Journ. f¨ur
die r …
3
votes
Accepted
Does a universal Frobenius map exist?
I don't really get the categorical picture of what you are asking, but it feels something very similar to the relation between finite fields of characteristic $p$ and the ring (of characteristic 0) of …
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. …