The top student must be diligent

There is a feeling of intangible joy and anger in it.

Of course, maybe it's because he already has a plan?

Xiao Yi continued to listen, and at the same time, he combined it with Mochizuki Shinichi's paper that he had read before, thinking about it in his mind, and occasionally turning over the A4 paper in his hand.

Anyway, although he is sitting here now, because the seat is arranged in the corner, he can be regarded as a small transparent person on the main table.

The reason why Schulz placed him here is just because of the significance of his paper as a "trigger" for this discussion. As for whether he can provide any useful opinions on this discussion, it is estimated that no one present can Haven't even considered it.

In this way, time passed quickly.

Schultz also began raising his formal questions.

"The first point is Frey's curve."

"Mochizuki describes all inequalities with a fixed d≥1 that reduce to all number fields k of degree [k:Q]≤d and all elliptic curves E/k corresponding to the point P∈Mell(k)..."

"...Using local Tate homogenization (rig m→Grig m /qZv′(E×k kv)rig, we obtain the set of local Tate parameters qv∈kv at the finite position v..."

"...However, please note that the degree of the boundary ∞ = (Mell Mell) is 1/2, and the degree of the logarithmic differential is 1/12, which cannot explain the reason for the sixth element I mentioned earlier."

…

Upon hearing this, more than 90% of the people present were confused about what Schulz was talking about, but those who could really understand it were brightened.

This should be the new point of doubt discovered by Schulz!

This questioning point is different from those he raised two years ago, but is more pointed and goes straight to the essence!

How does Mochizuki Shinichi explain it?

However, before Schultz could continue, Mochizuki stood up.

"I'm sorry, Peter, since you plan to mention it point by point, then I will also respond point by point."

"As for the first question you mentioned, the contradiction in the sixth element caused by the Frey curve and Tate analysis."

Mochizuki Shinichi left his seat and walked to the big blackboard - Xiao Yi finally discovered that there was an oversized blackboard in almost every room of the Max Planck Institute of Mathematics.

Mochizuki Shinichi picked up the blackboard pen from the side and started writing directly on it.

【Grm→Grm/qZv(E×k kv)r】

【deg(qE)=1[k:Q]∑v(qv)log(N (v))】

【h(P)=1/6deg(qE)+O(h(P)^1/2+1)】

【……】

After a few simple steps, Mochizuki Shinichi put down his pen and said, "My explanation is complete."

People present bared their teeth.

Have you finished explaining now?

Who can understand it at once without saying a word? ?

Of course, this is actually Mochizuki Shinichi's character. He acts very casually, rarely explains anything, and is always willful. However, this has aroused the envy of many young students, who are envious of his "obedience". "If you don't explain," others will take advantage of him because he can't help it.

However, there are still people present who can understand, and Schultz is one of them.

He frowned in thought and quickly understood the meaning of Mochizuki Shinichi's expressions.

Just like him, the effect was achieved by borrowing all the analysis methods from Xiao Yi's paper.

Solved his first problem.

He let out a sigh of relief. It seemed that today was going to be another fierce collision of mathematical ideas.

Then, he will no longer restrain himself.

"Yes, Professor Mochizuki, you did give a good explanation."

"Of course, this is not the only problem I have."

"The second question comes from your paper, IUTT-4, Theorem 1.10."

"Determine a natural number d≥1, there is a function αd, βd:N→R depends on d, such that αd→0..."

"So how do you use your IUTT to make your inequality hold?"

As for this question, Mochizuki Shinichi had obviously already prepared it, and he also started writing on the blackboard.

The two men's confrontation left only their voices in the entire conference hall.

No third party is involved.

Everyone else almost held their breath as they watched the debate in front of them that could probably be recorded in the history of mathematics.

Almost every questioning point raised by Schultz can make those who understand it show a look of sudden realization, and be surprised in their hearts at the advanced nature of this kind of mistake - it is difficult to detect.

However, Mochizuki Shinichi is well prepared. For almost every problem, he can solve it by just writing a line of formulas on the blackboard.

Only for a few questions would he reluctantly speak out to explain.

In this way, time passed slowly.

Compared to the solemn mood of other viewers, there was one person who had a different feeling.

This person was Xiao Yi. As he listened to the arguments of the two big guys, he felt more and more familiar with their way of thinking. At the same time, their questions and answers constantly allowed him to connect with the knowledge in his mind.

till the end.

…

【Gv o×μkv×((qj2v )j=1,.,*)N】

"I'm done explaining."

"Peter, do you have any more questions?"

Mochizuki Shinichi once again gave his answer on the blackboard.

This time, however, Schultz was silent.

Almost all the problems he found for this meeting were cleverly resolved by Mochizuki Shinichi. Only a few were still controversial, but he could not raise any further questions.

So, where is the problem?

Could it be that this discussion will end in vain again?

Mochizuki Shinichi...

He is indeed a person that Professor Faltings also considers "smart".

Sure enough, it's still so difficult.

The audience also remained silent.

The big guys at the main table also remained silent.

Onlookers could see that Schultz had tried his best.

Even more than five hours have passed!

No one present had lunch, but no one wanted to leave.

Are the results of this discussion about to come out?

However, after a long silence.

Suddenly there was a slightly nervous voice.

"Professor Schultz, Professor Mochizuki, maybe we can go back to the beginning and think about it?"

"If according to what Professor Mochizuki just explained on the fifth question, in any case, a [Hodge Theater] is abstractly derived from the data of a fixed once-truncated elliptic curve X; from the point that its only object is X and its state Projection is an automorphic category of X, which is equivalent to the natural functor of the [Hodge Theater] category.”

"So, starting from this perspective, let's go back to the third question. The content of far Abelian geometry is discussed here."

"We all know that far-Abelian geometry studies the absolute Galois group of rational numbers and the flattened fundamental group of any algebraic variety. The parts of them that are 'far away from Abelian' are the parts that do not comply with the commutative law ab=ba. How will it affect the properties of the corresponding algebraic structures?"

"In this case, in the sense that geometry and group theory are equivalent, far Abelian geometry will not hold -"

"In other words, it violates Professor Mochizuki's [Mochizuki Theorem]?"

Chapter 65 Let’s start from the beginning

In this empty meeting hall.

in this quiet space.

Hundreds of years ago, this may have been a place of worship for members of the Holy Roman Empire Church, and what sounded was the holy sounds of devout believers worshiping God.

Or, it may be the Symphony of Destiny. Although Beethoven left Bonn and never returned to his hometown, his soul after his death may come to his hometown in person to listen to his proud song being performed here. Work, the sound of fate knocking on the door.

Then a hundred years ago, this place became a busy post office, where all letters from up and down the city were collected and distributed. Perhaps what was heard was the anxious sound of people eager to get news from their family members far away.

Twenty years ago, what sounded here became the voice of the universe, because mathematics is the language of the universe, and tiny beings try to pry into the language of the universe and make discussions.

Today, this prying discussion started again.

However, when that nervous and young voice sounded, the results of this "snooping" seemed to begin to be announced.

Hundreds of eyes in the audience looked at the place where the sound came from.

And the young man's face finally came into everyone's eyes.