Chapter 460

Something interesting?

Many mathematicians have a slightly puzzled expression.

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

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

[Let A be the topological ring, and A is a continuous group homomorphism represented by the n-dimensional Galois.] Rule:

Homomorphic mapping: Gq→GLn(A)

Mapping: E^p^(n+1)→E[p^n]

Reverse limit: Tp(E):=limE[p^n]

Let Kp∞/Q be the extended domain of the kernel Kerρp corresponding to the above homomorphic map: ρp:Gq→GL2(Zp), i.e., ......]

Originally, the group of mathematicians in the audience were all holding their arms one by one, their eyes faintly sweeping the lines of formulas, and their expressions were unwavering.

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 unsettled.

Leaning forward one by one, their eyes meticulously scanning the strings of formulas written by Cheng Nuo, and at the same time there were words in their mouths, not knowing what they were saying.

【...... The absolute Galois group Gq acts on the Tate mode Tp(E) and satisfies αζ=ζ+1-|E(Ft)|. 】

Writing this, Cheng Nuo stopped writing.

Touching his chin and thinking for a few seconds, Cheng Nuo drew two horizontal lines under the last line of formula.

Knock knock!

Cheng Nuo tapped on the blackboard and pulled the mathematicians' thoughts back.

He pointed to the formula that filled half of the small blackboard, smiled and said, "That's the funny thing I'm talking about." ”

"To summarize simply, that is, if there is an elliptic curve E on Q, and L denotes the set of prime numbers with good reduction, then we can define an integer sequence of numbers (αζ) ζ∈L, that is, the DNA sequence of the elliptic curve, and the whole Ft rational point satisfying E is equal to the number of solutions to the equation + 1!"

As soon as Cheng Nuo's voice fell, the group of mathematicians below exchanged their heads and whispered among themselves.

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

Cheng Nuo shook his head, "No, it's not. Because I haven't figured out a way to prove it yet. However, I ran it on the institute's supercomputer and found that this formula holds up to 248,000. ”

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

Cheng's re-ring conjecture!

Many mathematicians couldn't help but widen their eyes.

It seems hard to believe why such a conjecture suddenly popped up for no reason.

As geometric mathematicians, especially the top ones in the world, they are naturally knowledgeable.

This "Cheng's Complex Ring Conjecture", they read the formula written by Cheng Nuo on the small blackboard several times from beginning to end, and they all looked dignified.

Cheng's complex loop conjecture is a method that uses Galois representation to closely link equations in finite fields with elliptic curves in complex number fields.

You must know that complex domain geometry has always belonged to the desert area in the field of geometry, although it is a general direction, but the research is too complicated, and the difficulty of producing results is too high, and no one is willing to study this direction painstakingly.

The complexity of complex domain geometry lies in the complexity of the complex torus in which it is represented.

Cheng's complex loop conjecture perfectly links the most common finite field equations with complex domain ellipses using formula relations.

It is equivalent to diverting a tributary of the ocean into the dry desert, giving this barren desert vitality and vitality.

No matter how dull their minds are, they understand the meaning of this conjecture.

It is no exaggeration to say that the academic significance of this Cheng Nuo conjecture is not even weaker than that of 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 the academic significance is still worse than several conjectures alongside it.

On the stage, Cheng Nuo stood leisurely.

In the audience, dozens of mathematicians had different expressions.

But on the other hand, the few Clay Institute of Mathematics personnel who came to preside over the progress report did not know whether to be happy or sad now.

The proposal of Cheng's complex loop conjecture is a great thing for the geometric community and even for the entire mathematical community.

But!

The purpose of their finally inviting Cheng Nuo is to prove the conjecture of Gushan Zhicun!

What now?

Taniyama Shimura's conjecture is not proven, so forget it. What's more, another conjecture was put forward!

The people at the Clay Institute of Mathematics were about to cry.

Originally, they were unable to prove eight conjectures, but now adding another one is simply forcing them to make this "purge plan" more difficult.

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

Professor Black's face was now blue and purple.

He found that he really underestimated Cheng Nuo.

Their "geometric conjecture" proves that the research results of the group in the past three months are not worth mentioning at all in the face of Cheng Nuo's "Cheng's complex ring conjecture".

But he didn't want this kid who was less than half his age to take up all the limelight of this report meeting, so after hesitating for a few seconds, he asked Cheng Nuo on the stage, "Mr. Cheng Nuo, your Cheng's complex conjecture does have great research value, but I can't figure it out, what is the connection between this and the Gushan Shimura conjecture you studied?"

"Mr. Black is a good question. Cheng Nuo's expression remained unchanged, and he said loudly, "At first glance, it seems that these two conjectures are not related in the slightest, but what I need to tell you is that these two conjectures are not only connected, but also extremely closely related. ”

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

"I am afraid that you will be familiar with this formula, which was used by Mr. Wiles when he proved Fermat's theorem. Its academic name is 'Frey's proposition'. ”

Using Frey's proposition as a bridge, we can perfectly combine Taniyama's Shimura conjecture with Cheng's complex ring conjecture. If the Gushan Shimura conjecture is not true, the rational point of the ellipse in the complex domain in Cheng's complex loop conjecture cannot be equal to the number of solutions of the finite field equation plus one. And vice versa!"

The mathematician with balding hair in the audience suddenly said, "That is to say, if the Gushan Shimura conjecture is established, the Cheng's complex ring conjecture is established, and if the Cheng's complex conjecture is established, the Gushan Shicun conjecture is established?"

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

Wow~!

The audience was in an uproar for the first time.

There are some young mathematicians, and the eyes that look at Cheng Nuo are already full of admiration.

Professor Black didn't raise his head, took out a piece of scratch paper and quickly calculated it according to the method described by Cheng Nuo, and finally found that the truth was as Cheng Nuo had come out.

The Taniyama Shimura conjecture and the Cheng's Fuhuan conjecture are one, and if one is established, the other will definitely be true.

Therefore, Cheng Nuo's work does not require all two proofs, only one of them needs to be proved.

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