"Hodge Theater's discussion objects mainly include two categories."
"'etale-like object' and 'Frobenius-like objects'."
"Roughly speaking, the former, which we usually denote as D, is given by the abstract topological group π1(X), which is considered to be an internal automorphism group. Likewise, as told in IUTT theory, we can consider finite etale coverage of abstract Galois categories without choosing base points."
"..."
Xiao Yi's narration begins.
His tone was slow but powerful.
He seemed to be very confident. Even if he slowed down and allowed so many mathematicians present to think carefully about what he said, he was not worried that any errors would be discovered.
The people present also followed his slow narration and analyzed it carefully.
Although he didn't really believe that Xiao Yi's idea would be the final word to end this debate, Schultz allowed him to continue speaking anyway, and Shinichi Mochizuki did not directly point out his mistake. On the contrary, judging from his expression, he seemed to feel surprisingly stumped.
Coupled with the confidence with which the young man spoke slowly...
Maybe, a miracle will really happen?
Of course, in their eyes, Xiao Yi spoke slowly because of his confidence, but in fact it was because this was his first English speech, and it was an English speech for a mathematics major, so he slowed down to prevent himself from making mistakes.
However, he still has confidence in his idea.
In fact, after listening to Schultz and Shinichi Mochizuki on the fifth question, he realized something was wrong.
Their argument used his ideas in "Non-singular Analytic and Absolute Remote Abelian Conjecture".
Therefore, not only can he understand, but he can also understand how they came to the corresponding conclusions.
Although he had not read the IUTT paper of Shinichi Mochizuki, which was more than 600 pages and took less than a month. In addition, it was obscure and difficult to understand. He only read the content related to Far Abelian Geometry. After all, he was familiar with Far Abelian Geometry.
As for other contents, the understanding is not so thorough.
But in the end, even if it was not thorough, it made him familiar with these theories.
Therefore, when Shinichi Mochizuki pointed out that "Hodge Theater is data abstractly derived from a fixed once-truncated elliptic curve X", he realized the problem.
"Suppose Cp, g is a hyperbolic algebraic curve with genus g on p-adic field K. Then the K-automorphism group of Cp, g is naturally isomorphic to its geometric etale basic group Γ=π1^et, the continuous automorphism group of geo(Cp, g)."
"This theorem is an important theorem proved by Professor Mochizuki on Far Abelian Geometry in 1999."
"Refer to the previous content again..."
Speaking of this, Xiao Yi suddenly paused for a moment and asked, "Maybe I can use the blackboard?"
"Huh?"
Schultz didn't react for a while. After hearing Xiao Yi's words clearly, he quickly said, "Of course, it's absolutely fine. In this house, whoever holds the microphone can use the blackboard."
"Thank you!"
Xiao Yi nodded and walked to the blackboard.
Finally, we can use the blackboard. The previous theories can be described orally, but the following content really needs to be explained using mathematical formulas.
He found a blank space and began to write.
[|X|=(lim←Z |G(Z)|)/πalg 1 (X)]
[...]
As soon as he got the blackboard, he seemed to have returned to a familiar environment. In a few clicks, he finished writing on the remaining blank areas on the blackboard.
But he didn't stop there. Instead, he took out the blackboard brush and erased what Schultz and Shinichi Mochizuki had just written.
An ordinary college student erased the blackboard writings of a Fields Medal winner and a Far Abelian Geometry master during the debate, which sounds a bit presumptuous.
However, no one cares about these things at this time. Compared with what Xiao Yi wrote, those blackboard writings are just blackboard writings, which are too insignificant.
In this way, time passed slowly.
Schultz's expression, which had been holding his chin in thought, gradually became enlightened.
On the main table, the corners of Faltings's mouth also turned up slightly. He had gradually understood Xiao Yi's thoughts.
Then he looked at the person next to him and said to him, "This kid is very smart, isn't he?"
The person next to him is also a Japanese, from Kyoto University like Shinichi Mochizuki.
Shigefumi Mori, the winner of Fields Medal, the previous chairman of International Mathematical Union.
Although Shigefumi Mori is not a supporter of the Shinichi Mochizuki proof, he is here today to give Shinichi Mochizuki a platform. At least, Shinichi Mochizuki will not be overpowered by the European mathematics community because he works alone.
Japanese mathematicians are relatively united.
But obviously, today's Shinichi Mochizuki, even if he was not suppressed by others, was accidentally knocked down by a 17-year-old child.
Hearing Faltings's question, he did not answer, but said, "You once said that Mochizuki is smart."
Faltings smiled, "He has always been very smart, otherwise he would not have become my student."
"But my criteria for smartness change based on the smart people I meet."
Shigefumi Mori directly stated his subtext. "So now you think this child is smarter than Mochizuki."
Faltings asked, "You don't think so?"
Shigefumi Mori was silent, then nodded. "Although I don't want to answer, I have to admit that you are probably right."
He looked at Shinichi Mochizuki, the 51-year-old master Far Abelian Geometry, who was once extremely confident in his own proofs. At this time, his expression gradually became depressed.
After all, the kid took out his own [Mochizuki Theorem] to prove his mistake.
And the logic is so clear that it is completely impossible to get around it.
Under this logic, there are only two possibilities for the final result. First, either the IUTT theory is wrong, or Mochizuki Theorem is wrong.
Faltings smiled softly and looked at Xiao Yi again.
"Young mathematicians, let's make mathematics interesting."
"... Therefore, in the end we can clearly find that unless the conditions of Mochizuki Theorem change, the inference of Hodge Theater can be established."
"But obviously, Mochizuki Theorem cannot be changed."
"So, the inference of Hodge Theater is not valid."
"Naturally..."
Xiao Yi did not continue, because I believe everyone present knows what is coming next.
But someone gave him the answer.
"The IUTT theory does not hold true."
Speaker, Shinichi Mochizuki.
"You're right."
The assembly hall went quiet for a moment.
Then, a burst of applause sounded, it was Faltings.
Other applause also broke out.
Gradually the whole conference hall was shaken.
Can I ask for a ticket?