After opening the mailbox, Xiao Yi saw that he had received a new email, and the email address shown as the sender was also the mailbox of Professor Maynard.
The reply was pretty quick!
Enter the mail.
[Mr. Xiao, hello!
I am very happy to receive your letter. I am very interested in the ideas you mentioned in your letter, especially the possibility of combining Far Abelian Geometry and Automorphic Forms as you described. I must say that this feels like a very bold move, but I have to admit that it is very consistent with the idea of Langlands Program.
So, I think there's a good chance.
My specific thoughts are mainly presented in the attachment. It should be noted that I don't know much about Far Abelian Geometry, so it is difficult to discuss with you from the aspect of Far Abelian Geometry. However, I do have a certain understanding of p-adic Hodge theory. Grothendieck once mentioned it. One speculation is that since the crystal homology H1(X/W(k))Qp of the special fiber and the p-adicétale homology H1(X, Qp) contain the same information, it is believed that there is a "mysterious functor". Although I cannot find out whether this mysterious functor is helpful to your idea for the time being, I always have an intuition that it should have some relationship.
Trust the intuition of a number theorist:)
Finally, I look forward to your reply.]
The attachment is also a PDF file with a title, called "Kuznetsov Trace Formula and p-adic Hodge theory".
After reading the other party's email, Xiao Yi immediately fell into deep thought.
"The mysterious functor?"
He really didn't know anything about this thing.
But after seeing Maynard put it forward, he suddenly had an intuition in his mind. It seemed that this thing might really have a great effect on his current research!
Mathematicians' intuition is sometimes very accurate, and this is especially true for particularly good mathematicians.
In Max Planck Institute for Mathematics's discussion, Xiao Yi was able to sensitively detect the problems in Shinichi Mochizuki's proof, which was inseparable from his intuition.
He immediately downloaded the attachment and started reading it.
In the attachment, Maynard mainly talked with him about Kuznetsov Trace Formula, which was the main method he used in the three papers in June.
Then we talked about some of the connections between this trace formula and p-adic Hodge theory, which are basically at the forefront of mathematics.
Similarly, it also brought a lot of inspiration to Xiao Yi.
This made Xiao Yi feel a little emotional in his heart. Although he had read many books and papers, such a simple exchange could bring him a lot of new things.
It seems that the knowledge he has is still slightly lacking.
Make a plan and read more books later.
Soon, Xiao Yi saw the end of this attachment, which had a total of more than 10 pages. At the end, Maynard finally gave Xiao Yi a complete introduction to the mysterious functor mentioned in the email.
"Frobenius homomorphism, Hodge filtration, K-tensor, and Galois group of K are all equivalent to the Barsotti-Tate group related to X?"
"For all clusters with good reduction on the p-adic domain, there should be a way to go directly from p-adicétale cohomology to crystallographic cohomology?"
Seeing these words, Xiao Yi's eyes suddenly lit up.
"Yes... that's it! From p-adicétale cohomology to crystal cohomology, as long as this can be achieved, I can contact Far Abelian Geometry from the perspective of Frobenius homomorphism!"
What a coincidence!
Xiao Yi's understanding of Frobenius homomorphism comes from Shinichi Mochizuki's IUTT theory. Hodge Theater proposed in this theory involves something called "Frobenius-like objects".
In an instant, many inspirations arose in his heart.
Afterwards, he immediately brought the scratch paper and began to carry out a long derivation along this line of thinking.
Perhaps, this derivation will be the key to ending all these problems!
Time passed quietly.
The news that Xiao Yi will hold a return report on September 26 spread quickly. At least, Shangjing's mathematical circles basically knew about it.
This kind of report back to the country is relatively normal.
People who go abroad to attend important academic conferences make reports on what they see and hear when they come back and pass them on to their domestic colleagues. After all, knowledge needs to be shared.
However, because the person giving the report this time is quite special. He is both the "terminator of the abc battle" who pointed out the most critical mistake of Shinichi Mochizuki at the Max Planck Institute, and he is also a 17-year-old Chinese genius who has been praised by many Philippine Prize bosses. Therefore, this report has become popular before it even started.
In the 2020 college mathematics class Joint Examination Group.
Qinghua-Jiang Long: [Screenshot]
Qinghua-Jiang Long: [Wori, guess what I saw?!]
People in the group quickly looked at the screenshot posted by Jiang Long.
This picture is a poster. It can be easily seen that it is a promotional picture for an academic report.
There is a photo of the reporter on it.
It is Xiao Yi!
Suddenly, this picture was like a bomb, blowing up all the divers in the group.
Shanghai Communications-Luo Xiao: [I'll go! This person looks like Scholar Xiao!]
[Shanghai Communications-Luo Xiao was banned by the administrator for 10 minutes]
Danfu-Xu Kangcheng: [Ah? Scholar Xiao This is a report? Scholar Xiao returned to China?]
Beijing University-Chen Muhua: [WTF? Is this true? Scholar Xiao If you go abroad, you can give an academic report when you come back? My day! Our military training is not over yet!]
USTC-Ye Cheng: [@USTC-Xiao Yi, Brother Xiao, you agreed to come back and participate in the last few days of military training with us, why do you have to stay out for ten days again!]
There was a heated discussion in the group, but as the real owner, Xiao Yi, even though he was liked almost a hundred times, he did not appear in the group.
People in the group also speculated that Xiao Yi was actually preparing a draft of the report, so he had no time to read it.
Unfortunately, they only guessed half of it, and they didn't know that what Xiao Yi was working on was something that could be regarded as a big deal in the world of mathematics.
Not long after the heated discussion in the group, suddenly, Chen Muhua appeared in the group again.
Beijing University-Chen Muhua: [Oh my God, brothers! I just got informed that on the day Scholar Xiao's report starts, students in our class can sign up to watch it!]
This news once again shocked other people.
Other students from Beijing University came out to confirm the news.
At this time, students from Qinghua and Jinghang also stood up and said that they had also received the news.
Suddenly, students from other schools became envious and jealous.
[Why! We want to go too!]
Beijing University-Chen Muhua: [Probably because Scholar Xiao's reporting location, Chinese Academy of Sciences Mathematics Research Institute is just across the street from our Beijing University? Qinghua and Jinghang are also very close to each other.]
[Damn it!]