universal data

Chapter 457 Cheng's Compound Ring Conjecture
460 chapter

interesting stuff?
Many mathematicians showed slightly puzzled expressions.

Cheng Nuo didn't mean to whet the appetite of the mathematicians.

He smiled, turned around, picked up a piece of chalk, and scribbled down a series of formulas on the small blackboard hanging on the side of the stage.

[Assume that A is a topological ring, and A is a continuous group homomorphism represented by n-dimensional Galois above.but:

Homomorphic mapping: Gq→GLn(A)
Mapping relationship: E^p^(n+1)→E[p^n]
Inverse limit: Tp(E):=limE[p^n]
Let Kp∞/Q be the extended field of kernel Kerρp corresponding to the above homomorphic mapping: ρp:Gq→GL2(Zp), that is to say...]

Originally, the group of mathematicians in the audience were holding their arms one by one, and their eyes glanced at the lines of formulas indifferently, with a calm expression on their faces.

They just wanted to see what new tricks Cheng Nuo could come up with.

But as time went on, the expressions on the faces of the mathematicians became less calm.

One by one leaning forward, their eyes meticulously scanned the string of formulas written by Cheng Nuo, and at the same time they were chanting words, not knowing what they were talking about.

【…The absolute Galois group Gq acts on the Tate module Tp(E), satisfying αζ=ζ+1-|E(Ft)|.】

After writing this, Cheng Nuo stopped writing.

After stroking his chin and thinking for a few seconds, Cheng Nuo carefully underlined two lines of horizontal lines under the last line of formula.

dong dong!

Cheng Nuo tapped on the blackboard to bring the mathematicians back to their thoughts.

He pointed at the formula that filled half of the small blackboard, smiled and said, "This is the interesting thing I was talking about."

"To summarize briefly, that is, if there exists E that is an elliptic curve on Q, and L represents a set of prime numbers with good reduction, then the integer sequence (αζ)ζ∈L can be defined, which is the DNA sequence of the elliptic curve , all Ft rational points that satisfy E are equal to the number of solutions to the equation + 1!"

As soon as Cheng Nuo finished speaking, the group of mathematicians below whispered to each other.

A mathematician raised his hand and asked, "Mr. Cheng Nuo, is this a new theorem you have derived?"

Cheng Nuo shook his head, "No, it's not. Because I haven't figured out a way to prove it yet. However, I have used the supercomputer of the research institute to run it, and found that this formula is valid within 248000."

"Because this formula explains the relationship between complex rings, I temporarily named it Cheng's complex ring conjecture!" Cheng Nuo explained with a smile.

Cheng's recirculation conjecture!

Many mathematicians could not help but widen their eyes.

It seems hard to believe why such a conjecture suddenly popped up out of nowhere.

As geometric mathematicians, especially those who are considered to be the top in the world, they naturally know the goods.

They read Cheng Nuo's formula written on the small blackboard several times from the beginning to the end of this "Cheng's compound circle conjecture", all of them looked solemn.

Cheng's complex ring conjecture uses the method of Galois representation to closely link the equation on the finite field with the elliptic curve on the complex number field.

You must know that complex number field geometry has always belonged to the desert area of ​​the geometric field. Although it is a general direction, it is too complicated to study and the difficulty of producing results is too high. No one is willing to study this direction painstakingly.

The complexity of complex field geometry lies in the complexity of representing the unit complex torus.

Cheng's complex ring conjecture perfectly connects the most common finite field equations and complex number field ellipses with formula relations.

It is equivalent to diverting a tributary of the vast ocean into the dry desert, making this barren desert full of vigor and vitality.

No matter how dull their brains are, they still understand the significance of this conjecture.

It is no exaggeration to say that the academic significance of this Cheng Nuo compound ring conjecture is not even weaker than Hodge's conjecture, which is listed as one of the seven major mathematical conjectures.

After all, the Hodge conjecture is only difficult to prove, and its academic significance is still worse than that of several conjectures juxtaposed with it.

On the stage, Cheng Nuo stood leisurely.

In the audience, dozens of mathematicians had different expressions.

But on the other hand, several people from the Clay Mathematics Institute who came to host the progress report meeting didn't know whether to be happy or sad now.

The proposal of Cheng's complex ring conjecture is a great thing for the geometry world, and even for the whole mathematics world.

but!

The reason they finally invited Cheng Nuo here was to prove Gu Shan Zhimura's conjecture!
What now?
Taniyama Shimura's conjecture has not been proven, so forget it.What's even more outrageous is that he came up with another conjecture!
Everyone at the Cray Math Institute was on the verge of tears.

Originally, they were powerless to prove eight conjectures, but adding one more now would simply increase the difficulty of their "cleaning plan".

…………

Professor Black's complexion is now blue and purple.

He realized that he had really underestimated Cheng Nuo.

Their "geometric conjecture" proves that the team's research results over the past three months are not worth mentioning in front of Cheng Nuo's "Cheng's compound loop conjecture".

But he didn't want this boy who was not half his age to take all the limelight of the report, so after hesitating for a few seconds, he asked Cheng Nuo on the stage, "Mr. Cheng Nuo, what is your progress?" The Trinite Complex Conjecture does have great research value, but I can’t figure out how it is related to the Taniyama-Shimura Conjecture that you are studying?”

"Mr. Black asked a very good question." Cheng Nuo said loudly without changing his expression, "Everyone, at first glance, it seems that these two conjectures are not related at all, but what I need to tell you is that there is a difference between the two conjectures. Not only is there a connection, but it's an incredibly strong connection."

Cheng Nuo scribbled a few formulas on the other half of the blank blackboard.

"I'm afraid you are familiar with this formula. When Mr. Wiles proved Fermat's last theorem, he used this series of formulas. Its academic name is 'Frey's Proposition'."

"Using the Frey proposition as a bridge, the Gushan Shimura conjecture and Cheng's complex ring conjecture can be perfectly combined. If the Gushan Shimura conjecture is not established, the rational point of the ellipse in the complex field of Cheng's complex ring conjecture cannot be equal to The number of solutions to a finite field equation is increased by one. And vice versa!"

A balding mathematician in the audience suddenly said, "That is to say, if Gushan Shimura's conjecture is true, then Cheng's complex ring conjecture is true, and if Cheng's complex ring conjecture is true, then Gushan Shimura's conjecture is true?"

Cheng Nuo pointed at the mathematician, "That's right, that's it!"

Wow~!

There was an uproar in the audience for the first time.

There were some young mathematicians who looked at Cheng Nuo with admiration in their eyes.

Without raising his head, Professor Black took out a piece of draft paper and quickly calculated according to the method Cheng Nuo described, and finally found out with frustration that the facts were exactly as Cheng Nuo said.

Taniyama Shimura's conjecture and Cheng's complex ring conjecture are integrated, if one is established, the other will definitely be established.

Therefore, Cheng Nuo's work does not require both proofs, but only one of them.

…………

(End of this chapter)