Chapter 480

Cheng Nuo tentatively named his newly derived theorem "Elliptic Abel's Group Theorem".

With the Elliptic Albert Group Theorem, the proof of the BSD conjecture can be continued.

"Senior brother, I'm sorry for you next. ”

"Hmm. Give me a week, oh no, four days, and I'll give you the results. ”

The emergence of the elliptical Albert group made Zhang Wei really see the hope of overcoming the BSD conjecture.

He had decided to put his other job off and focus all his energy on the BSD conjecture.

After all, once the BSD conjecture is proven, the benefits he can get are thousands of times higher than his other project.

............

The proof of the BSD conjecture is well underway.

Cheng Nuo and Zhang Weishi, two brothers, in addition to their daily work with graduate students, put all their remaining energy on this.

Soak in the office every day, there is no need to even go out.

This kind of workaholic attitude has invisibly brought pressure to many professors in Tsinghua University.

On one side, it was Cheng Nuo and Zhang Wei, the two brothers, who were so busy that they even trotted to the cafeteria to eat.

On the other side, a group of professors sat leisurely in the office drinking tea and chatting.

In an instant, the judgment is made!

So, almost in just a few days, many professors suddenly became active while working on projects.

That kind of long-lost hard work appeared on them again.

While the school's scientific research atmosphere is slowly changing under the influence of Cheng Nuo, Cheng Nuo and Zhang Wei are having a heated discussion in the office.

If you do the math, it has been almost four months since the BSD conjecture proof project began.

In this four-month period, Cheng Nuo and Zhang Wei finally completed the first piece of the puzzle of BSD's conjecture.

Prove the ultimate goal of the BSD conjecture, progress 1/3.

The two pieces of the puzzle are the Abel cluster and the modal group.

According to the framework, the next piece of the puzzle that needs to be solved is the modal group.

The modal group, which in the BSD conjecture is a finitely generated commutative group, exists in the same global domain as the elliptic curve.

What the two are now discussing is what the next stage of entry is.

Zhang Wei believes that the study should be carried out from the modal theorem of the Modal group, because when mathematicians studied this part of the BSD conjecture, they did it in depth.

And Cheng Nuo's view is different.

Cheng Nuo does not deny the views of mathematicians who have studied the BSD conjecture in the past, but he does not agree with it.

Since it has not really been proven, it is said that the previous reasoning scheme may not be correct.

Instead of following the old path of our predecessors, it is better to find another way and walk out of our own broad road.

Compared with the modulus theorem, Cheng Nuo believes that the remainder problem is a better way to start.

The final result of the argument was that Cheng Nuo persuaded Zhang Wei.

The next few months were spent trying to figure out the second piece of the puzzle.

............

Midsummer, a morning that is no longer normal.

On the plastic track of Tsinghua North Playground, Cheng Nuo wore headphones and jogged at a constant speed.

"Good morning, Professor!"

A voice sounded, followed by a figure that appeared in Cheng Nuo's sight.

This person is none other than Cheng Nuo's student who likes to pat his ass, Zhang Minghua.

Thinking of the impression that this student has brought to him for more than half a year, Cheng Nuo can only describe it in two words: speechless.

"Hmm. Cheng Nuo nodded, as if he had said hello.

Zhang Minghua didn't look like leaving, and while running side by side with Cheng Nuo, he said with an expression of admiration, "Professor, I didn't expect you to be so busy with work and take time out to exercise, no wonder you can become the youngest winner of the Wiblen Prize." Teachers like you should be a role model for our generation!"

"Uh......" Cheng Nuo was a little embarrassed to be licked, and said with a smile, "I heard Fan Yi say that your graduation thesis is about to be completed, which is very good!"

A graduation thesis is a thousand difficulties in our eyes, but in your eyes, it is just a matter of using your brain, and this little thing is not worth mentioning in front of you. ”

"After you finish your thesis, are you going to study in another country, or do you stay and work on a project with me?"

"Staying with you, of course. Zhang Minghua replied without hesitation, "In my opinion, none of those mathematicians abroad is better than teaching you, in my eyes, you are the biggest boss in the mathematics world, I don't need to go abroad, just follow you!"

Looking at Zhang Minghua's awe-inspiring appearance, Cheng Nuo was a little unsure, was Zhang Minghua licking those words, or was it really from the bottom of his heart?

"Show me your graduation thesis after you finish it, if you can't even pass this level, I won't let you participate in the graduation defense. Cheng Nuo's tone was light, "Another reminder to you, I'm very strict!"

"Professor, you don't know, I just like strict teachers!" Zhang Minghua showed a row of neat white teeth, "The stricter you treat students, the more you attach importance to students!" Professor, you are an admirable teacher, and I am honored to be your student!"

Cheng Nuo: "......"

Some of the licks were really unbearable, Cheng Nuo ran around twice without saying a word with his head down, and after returning to the apartment to take a shower, he went straight to the office of the research institute.

When Cheng Nuo arrived, Senior Brother Zhang Wei had just arrived.

"Senior brother, it's early!"

"Morning!"

"That's right. Cheng Nuo, I have compiled the sum of the square factors you want, come, you can see if there are any problems. ”

Cheng Nuo flipped it briefly, "Senior Brother Zhang, you did a good job." Over there, it's the problem of constructing rational points on an infinite-order curve, and I'll leave this to me. ”

"Cheng Nuo, this ......" Zhang Wei hesitated.

Cheng Nuo's problem of rational point construction on an infinite-order curve is the most critical part of the second puzzle, and it is also the most difficult part.

Cheng Nuo saw Zhang Wei's concern, shrugged his shoulders and said easily, "Senior brother, just leave it to me, I already have some ideas, and it shouldn't be a problem to actually deduce it." ”

"Then, trouble Cheng Nuo. ”

............

Cheng Nuo took a pen and calculated on scratch paper.

The object of study is the representation of the rational points obtained by the congruent of the Modal exchange group when it intersects with an infinite order curve.

This is a rather complex issue, but fortunately, Cheng Nuo has already had some inspiration.

These inspirations came when Cheng Nuo was running in the playground these mornings.

So he got into the habit of going to the playground twice a morning.

Assuming that D has no square factor, a simple elementary consideration shows that D is the same remainder equivalent to the elliptic curve E_D: y^2=x^3-D^2x has a rational point of y \neq 0 on it. It can be proved that such a point does not belong to T, so D is the same remainder and equivalent to r_D>0, and all the same remainders D are determined, such that r_D> 0, and then ...... In this way, it can be determined that this rational point is ......"

"Alas, no, wait!"

Suddenly, Cheng Nuo's pen stopped, and his eyes were slightly condensed.

The corners of his mouth curled, and he muttered, "I seem, I have found something amazing." ”