universal data

Chapter 318 Discussion
321 chapter

After returning to the dormitory from Professor Fang's apartment, Cheng Nuo immediately searched the Internet for some news about the BSD conjecture.

Sure enough, he found out that four years ago, a British mathematician named Zhan Qi and another German mathematician named Sulti collaborated to solve the problem of proving that when the analytic rank is zero, The weak BSD conjecture is a breakthrough in the generalized BSD conjecture.

However, since then, few people in the mathematics community have published important results that are helpful to the proof of the BSD conjecture, and the progress of research has been hindered for a while.

The proof work of Professor Fang's "weak BSD conjecture when the analytical rank is 1" can barely be regarded as the other half of the unproven weak BSD conjecture.

As long as Professor Fang can prove that "when the analytic rank is 1, the weak BSD conjecture holds except for 2 and derivation", basically all the weak BSD conjectures are proved.

But... there is no money for this!
The reward condition proposed by the Clay Mathematics Institute is to completely solve the BSD conjecture.The weak BSD conjectures that it is just a small guard BOSS next to the world's big BOSS. Defeating him can only be regarded as an appetizer. The reward items are only experience points and no gold coins.

The more he browsed the news about the BSD conjecture on the Internet, the more panicked Cheng Nuo became.

According to the above, since the research results that the weak BSD conjecture holds when the analytical rank is 0 were published, some mathematical experts around the world have tried to overcome the other half of the weak BSD conjecture, and believe that this is not What a difficult thing to do.

In their view, it is OK to just follow the deduction method of Jench and Sulti, substituting the analytical rank of 1 into it and re-deriving it again.

But they didn't think that if Jench and Sulti could use the same method to deduce and prove another situation, why not just wait for the weak BSD conjecture to be fully proved before claiming it to the outside world.Wouldn't that get more fame and attention?

The two of them did not do this, and they can only prove that the proof work of the weak BSD conjecture in the two cases is not suitable for the same theoretical system.

Therefore, four years have passed, and no one has made a big splash in the research work of BSD.

"It's really a troublesome thing!" Cheng Nuo closed the computer, sat on the chair in front of the desk in the dormitory, put his hands on his pillow, and murmured to himself.

He glanced at the few drafts on the desk that the professor asked him to bring back before he left.

This thing can be regarded as the research effort of Professor Fang on the BSD conjecture in the past two years.

There are a dozen or so pages of draft paper, but the level is extremely slow.

It's not because Cheng Nuo wants to work slowly and meticulously, but... There are so many things that I can't understand at all!

Such as "L-level functions of elliptic curves", "Abelian varieties", "Model's theorem"... Although he has dabbled in this series of knowledge, he is obviously far behind when it comes to proficient application and formula derivation. some heat.

When the book is used up, I hate it less!
This is how Cheng Nuo feels now.

He put the draft on the desk in frustration, not going to read it for now.If you look at it again, you still can’t understand it, and there is no benefit other than wasting a lot of brain cells.It's better to read more books and store some professional knowledge about BSD conjecture.

Anyway, Professor Fang said that the work of proving this conjecture is not urgent.

There are probably millions of mathematicians all over the world who are bored in their huts thinking hard about how to prove the BSD conjecture and get a prize of 100 million US dollars.But there are only a few who are really capable, and even those few people, it doesn't mean that whoever studies it early will be the first to solve the conjecture.

Everything depends on fate.

Fate is here, even if you study for a year, I am afraid that you can think of proof methods earlier than those who have studied for ten years.

…………

In the following week, Cheng Nuo became a frequent visitor to the library of Tsinghua University.

Basically, Cheng Nuo took over all the books and periodicals related to the BSD conjecture, such as "Modern Mathematics", "Mathematical Analysis of the Whole Domain", and "The Labeling of Elliptic Curves".

In the past, Cheng Nuo didn't deliberately and systematically study the relevant knowledge in this field, but once his brain speed is fully opened, and he has a week to fully absorb knowledge from books, the progress is enough to be described as lightning fast.

A week later, Cheng Nuo was able to understand most of the formulas in Professor Fang's draft.At the same time, another unfinished project in Cheng Nuo's hands, "Simulation of Electron Cyclotron Heating and Current Drive Based on the Three-dimensional Fokker-Planck Equation", has also entered the final work.

The research progress of this electronic cyclotron wave project in cooperation with the Chinese Academy of Sciences can only be described as smooth.Except for a little trouble at the beginning, the rest went smoothly.

Anyway, the School of Mathematics and the School of Physics are divided into three non-stop rotations and alternating research, neither of which is willing to lose face of their respective schools. Once they get the task, they all start working with high morale as if they have been drugged.

The original half-year research period was also shortened to four months.

"Happy cooperation!"

"Happy cooperation!"

At the celebration banquet, the four smiled and shook hands.

Mathematics and science are not separated, and there will be many cooperation projects with the Academy of Physics in the future. It is hard to say that the four will not join the same research group again.Through this cooperation, the two seniors of the academy had a full understanding of the abilities of Cheng Nuo and Wang Genji.

Especially Cheng Nuo.They knew that apart from this project, Cheng Nuo was also working as the deputy leader of another project group in the School of Mathematics, and the inside story of that project had already competed with the time competition at the University of California, Berkeley. I have heard some more or less.

It's not admiration, but it's a recognition of Cheng Nuo, a freshman.If there was a chance to cooperate next time, they wouldn't mind bringing Cheng Nuo in again.

And Cheng Nuo didn't have time to talk about it.After the celebration banquet, Cheng Nuo went to Professor Fang's office in the building of the Mathematical Academy to discuss the specific proof work of the conjecture.

During the discussion, Professor Fang was basically talking and Cheng Nuo was listening.

What Professor Yi Fang has learned after two years of immersion in this field is obviously not comparable to that of Cheng Nuo, who only studied for less than half a month.

From flesh and blood to bones, Professor Fang spent the whole morning explaining to Cheng Nuo step by step the complexity of the BSD proof work, as well as the proof idea of ​​the other half of the BSD conjecture that Professor Fang conceived.

"Still starting from the elliptic curve in the rational number field, combined with the finiteness of the order of the Shafarevich-Tate group, it is concluded that if E is an elliptic curve with complex multiplication, then there is L(E, 1)≠0→r (E)=0, and finally get a Bloch-Kato conjecture, in theory, it can be deduced that the weak BSD conjecture is valid except for 2."

Professor Fang concluded.

(End of this chapter)