The top student must be diligent.

Chapter 83 Yes, that’s it!
"What did you say?"

When Ma Zhiyuan heard Xi Lan's words, he was stunned, thinking that he didn't hear it clearly.

This young man on the stage knows more about number theory than they thought?
Xi Lan shook her head, pointed at the PPT, and said, "We'll know soon."

Ma Zhiyuan looked at the PPT in the direction of his finger, and then his eyes narrowed.

At this time, the PPT on the stage had been turned to another page, and the theme of this page was "The connection between far Abelian geometry and number theory."

"What does he want to do?" Ma Zhiyuan became more curious about what the young man wanted to do.

At the same time, other mathematicians who noticed the content of this page of the PPT also became confused.

"Mr. Hu, what is your student going to talk about?"

Sitting on the other side of the seat, Hu Guangde's arch-enemy, Academician Liao Huan from Shanghai University, was also present. After seeing the content on this page of the PPT, he immediately turned around and asked Hu Guangde next to him.

Hu Guangde glared at him and said, "Mr. Liao, please show some respect to me. I am an academician."

"What you said is not the same as mine." Liao Huan shrugged, looking indifferent.

The two men locked eyes, and it was as if an electric current was crossing between their sights.

At this moment they all wanted to know who had arranged for the two of them to sit together.

Otherwise, wouldn’t it be equivalent to arranging Palestine and Israel together during international conferences?

Finally, Hu Guangde snorted coldly: "Don't worry, what Xiao Yi is going to say later will definitely scare you."

"I guess you don't know it yourself!" Liao Huan clicked his tongue.

Hu Guangde laughed: "So what if I don't know? Xiao Yi can study whatever he wants. He is capable of studying any difficult problem in mathematics."

"I just need to believe that what he has come up with must be something you can't come up with."

“You fucking…” Liao Huan’s eyes widened again, and he snorted, “You talk as if you could figure it out.”

"I can't figure it out, but they are still my students." Hu Guangde didn't care and said happily.

Liao Huan stopped talking.

Damn, why am I so envious?

Couldn't their school's admissions office have been more resolute in its stance and recruited the kid on the stage into their school?
……

Xiao Yi on the stage had no idea that this page of his PPT had caused so many reactions from the audience.

However, the next part is indeed the most important part of his report.

"Although Professor Mochizuki's IUTT theory is wrong, we must know that Professor Mochizuki's idea of ​​developing far Abelian geometry and the mathematical ideas he demonstrated in the process are worth learning."

"Professor Mochizuki wants to use far Abelian geometry to solve the ABC conjecture. There is a core idea, which is to apply the former to the field of number theory."

"To briefly explain what tele-Abelian geometry is, in a very simple sentence, it is to consider how much information the etale fundamental group in algebraic geometry can give about the algebraic variety itself, and to what extent it can determine the isomorphism class of the algebraic variety itself."

"Information is very important for mathematical research. When changing into different forms, sometimes the mathematical information we need will be lost, but sometimes after changing into another form, some information will become clear, or even some new information will appear, which can help us solve some problems."

"Applying tele-Abelian geometry to number theory has this effect." "But now the question is, how does tele-Abelian geometry relate to number theory?"

“Then let us go back to a functor relation that Grothendieck proposed several decades ago.”

The ppt turned the page again, and the new page introduced the mysterious functor that brought infinite inspiration to Xiao Yi.

"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."

"And the Frobenius homomorphism and Hodge filtering, the K tensor, the Galois group of K are all equivalent to the Barsotti-Tate group associated with X."

"Based on these two premises, let us think about a possibility—"

"What happens if we introduce a ring Bcris with Gk action, a Frobenius φ, and a filtering after expanding the scalar from K0 to K?"

Xiao Yi walked to the blackboard again and started writing in the blank space on the right half.

【BcrisK0·HdR(X/K)≌BcrisQp·H(X·K，Qp)】

……

After he took a few simple steps, the scholars with a wider range of knowledge in the audience suddenly narrowed their eyes.

Many people may have heard of Grothendieck's mysterious functor, but fewer people understand it. However, among the many mathematicians present, there are still some who understand it.

The research history of this mysterious functor has been several decades. After all, it involves the possibility of unifying etale cohomology theory and crystal cohomology theory.

Going further, the discovery of the close connection between different cohomologies will be very helpful to the theory of motivation in algebraic geometry, [Motive], which was also developed by Grothendieck - to be more precise, this thing is not a theory, but an unproven proposition.

Its purpose is to find a "universal cohomology theory", and cohomology theory is an important tool in algebraic geometry and algebraic topology. Therefore, this theory is also of great significance to the mathematical community.

As a possible brick and mortar of the "theory of universal cohomology", the mysterious functor proposed by Grothendieck naturally attracted the research of many mathematicians. For example, Faltings is a mathematician who has been quite successful in this area.

However, decades later, the true appearance of this mysterious functor has still not been fully defined.

However, what Xiao Yi wrote now made those mathematics scholars who could understand it become serious.

Because now Xiao Yi is conducting a very in-depth analysis of this mysterious functor from the perspective of far Abelian geometry.

Time passed slowly as Xiao Yi told his story.

The blackboard was gradually filled with Xiao Yi's handwriting, until finally -

"So, we have successfully proved—"

【BstK0·HdR(X/K)≌BstQp·Het(X*K，Qp)】

Xiao Yi wrote down this line of equivalence in the last blank space on the blackboard.

“So we have finally found what this mysterious functor, (x, -) really looks like!”

As he wrote the last line of the formula, the mathematicians in the audience who understood it suddenly widened their eyes.

Yes, this is it!
This young man actually did it!
He successfully defined Grothendieck's mysterious functor and revealed its true face!

(End of this chapter)