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answered l-functions of calabi-yau varieties
Sep
18
comment Is the field of constructible numbers known to be decidable?
Write to Videla and ask him. He surely knows the state of the art and he will be happy to answer; he is a very nice person. As I understand, the problem is open and there is a group of people (including Videla) looking into it.
Sep
5
awarded  Yearling
Oct
23
awarded  Good Answer
Sep
17
awarded  Commentator
Sep
17
comment Philosophy behind Mochizuki's work on the ABC conjecture
(cont.) The table in page 27 of IUTT-I gives an idea of what are the roles played by some of the main objects introduced by Mochizuki (and as VD pointed out, the hyperbolic curve "is" the number field, not the elliptic curve). Anybody can read this directly from the paper, but the only reason why I am mentioning it is the following: I was very curious about the papers (as everybody else), but the first couple pages seemed very intimidating. However, after spending some time with the papers on Frobenioids then the introduction of IUTT-I became readable after all. I hope this suggestion helps!
Sep
17
comment Philosophy behind Mochizuki's work on the ABC conjecture
For people wanting to known more details without having to read all the 500 pages: the answer provided by VD is a nice survey of the first 16 pages of IUTT-I (avoiding technicalities of how the several types of Hodge theaters are actually constructed, or what are the prime-strips). For the interested reader, the first 27 pages of IUTT-I indeed give a very good introduction. However, it is better to get used with the language of Frobenioids FIRST, otherwise the exposition can be intimidating. Unfortunately, it does not hint on the actual "source of inequality" (I mean, not beyond analogies).
Sep
17
awarded  Nice Answer
Sep
17
awarded  Nice Answer
Sep
17
awarded  Critic
Sep
17
awarded  Supporter
Sep
17
awarded  Editor
Sep
16
comment undergraduate logic textbook
Very nice suggestion!
Sep
16
comment Philosophy behind Mochizuki's work on the ABC conjecture
@VD: I think one should read more carefully the hypothesis. Also, I would not be surprised if the final Diophatine statement is not 100% correct as stated and needs to be refined - it is such a long and complicated work!. However, I think that the whole point is the technique: if it is correct$-\epsilon$ then people will make it work at some point. I do not remember the solution of a BIG problem that was 100% correct the first time it was released (perhaps I am exaggerating a little bit).
Sep
16
comment Philosophy behind Mochizuki's work on the ABC conjecture
If you want to apply the theorem 1.10 with initial theta data having F=Q then you have a problem: F must contain i (square root of -1). If E was already semi-stable over Q then I guess that nothing happens, but otherwise the height of E gets smaller. Also, you need semi-stable reduction of E over F as part of the conditions. For example, for the Frey curve associated to an ABC triple to be semi-stable over Q, you need that the ABC triple (a,b,a+b) must be primitive (no common factor) and 16 must divide ab(a+b) (perhaps not 16...). This slightly reduces the list "too-good-to-be-true" examples.
Sep
11
comment Beautiful theorems with short proof
Zagier's paper "values of zeta functions and their applications" has a nice short proof of $\zeta(2)=\pi^2/6$ due to Calabi.
Sep
10
comment At what times were people interested in prime numbers
The Ishango bone is pretty old and curiously has some suspicious prime numbers on it. I'm adding this as a comment because of lack of reasons for considering it as relevant, but I could not resist. P.
Sep
10
revised Philosophy behind Mochizuki's work on the ABC conjecture
added 52 characters in body
Sep
10
comment Mochizuki's proof and Siegel zeros
@GH: Perhaps the word "clearly" should be omitted in my post. Once I heard that the word "clearly" should be omitted in all the mathematical literature: if something is "so clear" then it is pointless to say that it is clear, while on the other hand if we use the word "clearly" to hide an argument that we don't want to write then we should perhaps be honest and at least give some hint. In this case, what I meant is that Theorem A alone (modulo notation) gives the main result without having to prove further propositions before using it. In any case, sorry about using the word "clearly".
Sep
9
revised Mochizuki's proof and Siegel zeros
added 1869 characters in body