The top student must be diligent.

Chapter 66 You are right

Chapter 66 You are right
“The discussion subjects of Hodge Cinema mainly include two categories.”

"'Etale-like object' and 'Frobenius-like object'."

"Roughly speaking, the former, which we usually denote as D, is given by the abstract topological group π1(X), considered to be a group of internal automorphisms, and similarly, as in IUTT theory, we can consider finite etale covers of abstract Galois categories without having to choose a basis point."

"..."

Xiao Yi's story begins.

His tone was slow but powerful.

He seemed very confident that what he said would be discovered without any worries, even if he slowed down and allowed so many mathematicians present to think carefully about it.

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 conclusion to end the debate, Schultz allowed him to continue anyway, and Mochizuki Shinichi did not directly point out his mistake. On the contrary, judging from his expression, he seemed to be surprisingly stumped.

Plus the confidence of this young man as he slowly tells the story...

Maybe, a miracle will really happen?
Of course, in their eyes, Xiao Yi spoke slowly because he was confident, 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 avoid making mistakes.

However, he still has confidence in his idea.

In fact, after listening to Schultz and Mochizuki Shinichi on the fifth question, he realized something was wrong.

Their debate used his ideas from "Non-Singularity Analysis and the Absolutely Tele-Abel Conjecture".

So, he could not only understand, but also understand how they came to the corresponding conclusions.

Although he was limited by the fact that he did not finish reading Shinichi Mochizuki's IUTT paper, after all, it was more than 600 pages, and there was only less than a month to do so. In addition, the paper was obscure and difficult to understand, so 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 he didn't understand them thoroughly, he became familiar with these theories.

So, when Shinichi Mochizuki pointed out that "Hodge Cinema is abstractly derived from the data of a fixed single-punctured elliptic curve X", he realized the problem.

"Assume that Cp,g is a hyperbolic algebraic curve of genus g over the p-adic field K. Then the K-automorphism group of Cp,g is naturally isomorphic to the continuous automorphism group of its geometric etale fundamental group Γ=π1^et,geo(Cp,g)."

"This theorem is an important theorem proved by Professor Mochizuki in 1999 in far-Abelian geometry."

"Referring to the previous content..."

At this point, Xiao Yi suddenly paused for a moment and asked, "Maybe I can use the blackboard?"

"what?"

Schultz didn't react for a moment. After hearing Xiao Yi's words clearly, he quickly said, "Of course, it's totally possible. In this house, whoever holds the microphone can use the blackboard."

"Thank you!"

Xiao Yi nodded and walked to the blackboard.

Finally I can use the blackboard. I can explain the previous theories 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 strokes, he finished writing on the remaining blank areas on the blackboard.

But he did not stop there. Instead, he took out the blackboard brush and erased what Schultz and Mochizuki Shinichi had just written.

It might sound a bit outrageous for an ordinary college student to erase the blackboard writing during a debate between a Fields Medal winner and a master of far-Abelian geometry.

However, no one cared about these things at this time. Compared with what Xiao Yi wrote, those blackboard writings were just blackboard writings, too - insignificant.

In this way, time passed slowly.

Schultz, who had been pinching his chin in thought, gradually came to a state of enlightenment. At the main table, Faltings' mouth corners also curled up slightly, and he 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, and like Mochizuki Shinichi, he is from Kyoto University.

Shigefumi Mori, Fields Medal winner and former president of the International Mathematical Union.

Although Mori Shigefumi is not a supporter of Mochizuki Shinichi's proof, he came here today to support Mochizuki Shinichi. At least, Mochizuki Shinichi will not be bullied by the European mathematics community because he is fighting alone.

Japanese mathematicians are relatively united.

But obviously, today, even though Shinichi Mochizuki was not bullied by others, he was unexpectedly knocked down by a 17-year-old child.

Hearing Faltings' question, he did not answer, but said: "You once said that Mochizuki is smart."

Faltings smiled and said, "He has always been very smart, otherwise he would not have become my student."

"But my criteria for what is smart changes depending on the smart people I meet."

Mori Shigefumi directly stated his subtext: "So now you think this child is smarter than Mochizuki."

Faltings asked back, "You don't think so?"

Mori Shigefumi was silent, then nodded: "Although I don't want to answer, I have to admit that you are probably right."

He looked at Mochizuki Shinichi, the 51-year-old master of far-Abelian geometry. He used to be extremely confident in his proof, but now his expression gradually became dejected.

After all, the child used his own [Mochizuki Theorem] to prove his mistake.

And the logic is so clear that it is completely impossible to circumvent it.

Under this logic, there are only two possible final results. First, either the IUTT theory is wrong, or the Mochizuki theorem is wrong.

Faltings smiled lightly and looked at Xiao Yi again.

“Young mathematicians, please make mathematics more interesting.”

……

" ... Therefore, in the end we can clearly see that unless the conditions of Mochizuki's theorem change, the corollary of Hodge Cinema can be established."

"But obviously, the Mochizuki Theorem cannot be changed."

"Therefore, Hodge Cinema's inference is not valid."

"nature……"

Xiao Yi did not continue speaking, because he believed that everyone present knew what was coming next.

But someone gave him an answer.

"The IUTT theory doesn't hold up."

The speaker is Shinichi Mochizuki.

"you are right."

The conference hall was silent for a moment.

Then, there was a round of applause. It was Faltings.

Other applause followed.

Gradually, the entire conference hall was shaking.