"What did you say?"
Hearing Xi Lan's words, Ma Zhiyuan was stunned and thought he didn't hear clearly.
This young man on the stage knows more about number theory than they thought?
Xi Lan shook his head, pointed at the ppt, and said, "We will know soon."
Ma Zhiyuan followed the direction of his finger and looked at the ppt, and then his eyes narrowed.
At this time, the ppt on the stage has been turned to another page, and the theme of this page is "The Connection between Far Abelian Geometry and Number Theory".
"What does he want to do?" Ma Zhiyuan became more curious about what this boy wanted to do.
At the same time, other mathematics scholars who noticed the contents of this ppt also had doubts in their hearts.
"Hu, what do you, the student, plan to say?"
On the other side of the seat, Hu Guangde's archrival, Academician Liao Huan from Shangjing University, was also present. After seeing the content on this ppt, he immediately turned around and asked Hu Guangde next to him.
Hu Guangde glared at him. "Liao, please show some respect to me, I am an academician."
"You're not talking about the same thing as me." Liao Huan shrugged, looking indifferent.
The two of them met their eyes, and it was as if electricity was flowing between their eyes.
At this time, they all wanted to know who arranged for the two of them to sit together.
Or is it equivalent to lining up Palestinian and Israeli National Security together at an international conference?
Finally, Hu Guangde snorted coldly, "Don't worry, what Xiao Yi is going to say later will definitely shock you."
"I don't think you know it yourself!" Liao Huan said with his tongue.
Hu Guangde laughed, "So what if I don't know? Xiao Yi can study whatever he wants. He has the ability to study any difficult problem in mathematics."
"I just need to believe that what he comes up with must be something you can't come up with."
"What the hell..." Liao Huan's eyes suddenly widened again, and he finally shouted, "You made it sound like you could do it."
"I can't figure it out, that's my student too." Hu Guangde said cheerfully without caring.
Liao Huan stopped talking.
Damn it, why am I so envious in my heart?
Couldn't their school's admissions office have been firmer in their original position and drag the kid on stage into their school?
Xiao Yi on the stage did not know that this page of his ppt caused so many reactions from the audience.
However, the most important part of his report did come next.
"Although Professor Shinichi Mochizuki's IUTT theory is wrong, what we must know is that Professor Mochizuki's idea of developing Far Abelian Geometry, and the mathematical ideas he displayed in the process, are worth learning."
"Professor Mochizuki wants to use Far Abelian Geometry to solve the abc conjecture. He has a core idea, which is to apply the former to the field of number theory."
"To briefly explain what Far Abelian Geometry is, in a very simple sentence, consider how much information the etale basic 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 a very important thing for the study of mathematics. Under different forms of changes, sometimes the mathematical information we need will be lost, and sometimes after transforming into another form, some information will become clear, and even some new information will appear, which can help us solve some problems."
"Applying Far Abelian Geometry to number theory has such an effect."
"But the question now is, how does Far Abel relate to number theory?"
"So, please let us go back to a functor relationship proposed by Grothendieck decades ago."
Turn the ppt page again, and a new page introduces 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 Frobenius homomorphism, Hodge filtration, K-tensor, and Galois group of K are all equivalent to the Barsotti-Tate group related to X."
"Based on these two premises, let us think about a possibility——"
"What happens if we introduce a ring Bcris with Gk action, a Frobeniusφ, and a filter after extending the scalar from K0 to K?"
Xiao Yi walked to the blackboard again and wrote 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 in the audience who had a relatively wide range of knowledge suddenly narrowed their eyes.
Grothendieck's mysterious functor may have been heard by many people, but fewer people understand it. However, among the many mathematics scholars present, there are still some people who understand it.
There has been research on this mysterious functor for decades. After all, this thing involves the possibility of unifying etale cohomology theory and crystal cohomology theory.
Furthermore, discovering the close connection between different cohomology will be very beneficial to Motive theory in Algebraic Geometry, [Motive]. This theory was also developed by Grothendieck - to be more rigorous, this thing is not a theory, but an unproven proposition.
The purpose is to find a "universal cohomology theory", and the cohomology theory is an important tool for Algebraic Geometry and Algebraic Topology. Therefore, this theory is also of great significance to the mathematical community.
As a possible building block of the "universal cohomology theory", the mysterious functor proposed by Grothendieck has naturally attracted the research of many mathematicians. For example, Faltings is a mathematician who has been more successful in this regard.
However, decades have passed, and the true face of this mysterious functor has still not been completely defined.
However, what Xiao Yi has written now makes these mathematical scholars who can understand 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 gradually passed as Xiao Yi narrated.
The blackboard was gradually occupied by Xiao Yi's handwriting, until finally——
"So, we successfully obtained the certificate——"
[BstK0·HdR(X/K)≌BstQp·Het(X*K, Qp)]
Xiao Yi Write this line of equivalent equations in the last blank space on the blackboard.
"So, we finally found the true face of this mysterious functor, (x, -)!"
As he wrote the last line of formula, the eyes of the mathematicians in the audience who understood it widened.
Yes, this is it!
This young man actually did it!
He successfully defined the mysterious functor of Grothendieck and revealed its true face!