Chapter 460: Cheng's Conjecture

Chapter 460
Something interesting?
Many scientists showed a slightly puzzled expression.
Cheng Nuo didn't mean to jeopardize the appetite of mathematicians.
He smiled, turned around, took a piece of chalk, and wrote a series of formulas on the small blackboard hanging on the side of the stage.
[Suppose A is a topological ring, and A is a continuous group homomorphism represented by the upper n-dimensional Galois. then:
Homomorphic mapping: Gq→GLn(A)
Mapping relationship: E^p^(n+1)→E[p^n]
Reverse limit: Tp(E):=[p^n]
Let Kp∞/Q be the extended domain of Kerρp corresponding to the above homomorphic mapping: ρp:Gq→GL2(Zp), that is to say...]
Originally, the group of mathematicians in the audience held their arms one by one, their eyes faintly scanned the lines of formulas, and they looked unwavering.
They just want to see what new tricks Cheng Nuo can make.
But with the passage of time, the expressions on the faces of mathematicians became unstable.
Leaning forward one by one, they scrutinized the series of formulas written by Nuo with their eyes scrutinized, and at the same time they muttered words, not knowing what they were saying.
[...The absolute Galois group Gq acts on the Tate modulus Tp(E) and satisfies αζ=ζ+1-
E(Ft)
.]
At this point, Cheng Nuo stopped writing.
Touching his chin and thinking for a few seconds, Cheng Nuo heavily drew two horizontal lines under the last formula.
咚咚!
Cheng Nuo knocked on the blackboard to bring back the thoughts of the mathematicians.
He pointed to the formula that took up half of the small blackboard, smiled and said, "This is the funny thing I said."
"Simply summarized, that is, if there is an elliptic curve in E, and L represents a set of prime numbers that are reduced, the integer sequence (αζ)ζ∈L can be defined, which is the DNA sequence of the elliptic curve. , All Ft rational points satisfying E are equal to the number of equation solutions + 1!"
As soon as Cheng Nuo's voice fell, the group of mathematicians below whispered and whispered to each other.
A mathematician raised his hand and asked, "Mr. Cheng Nuo, is this your newly derived theorem?"
Cheng Nuo shook his head, "No, it's not. Because I haven't figured out a way to prove it. But I have run it on the supercomputer of the research institute and found that this formula is valid within 248,000."
"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 complex ring conjecture!
Many scientists can't help but stare.
It seems hard to believe why such a conjecture suddenly appeared inexplicably.
As geometric mathematicians, especially the top group 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, all with a solemn expression.
The Cheng's complex ring conjecture uses the method expressed by Galois to closely link the equations on the finite field with the elliptic curve on the complex number field.
You know, 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.
The complexity of the geometry of the complex number field lies in the complexity of the unit complex torus.
The Cheng's complex ring conjecture perfectly connects the most common finite field equations and complex number field ellipses using formula relations.
It is equivalent to diverting a tributary of the vast ocean into the dry desert, so that this barren desert will be full of vitality and vitality.
No matter how dull their brains are, they understand the meaning of this conjecture.
It is no exaggeration to say that the academic significance of this Cheng Nuo complex ring conjecture is not even weaker than Hodge's conjecture, which is listed as one of the seven mathematical conjectures.
After all, Hodge’s conjecture is only difficult to prove, and its academic significance is still worse than the parallel conjectures.
On the stage, Cheng Nuo stood leisurely.
In the audience, dozens of mathematicians had different expressions.
But on the other hand, the staff of the Cray Institute of Mathematics who came to chair the progress report didn't know whether they should be happy or sad now.
The proposal of the Cheng's complex ring conjecture is a great thing for the geometric world, and even for the entire mathematical world.
but!
The reason they finally invited Cheng Nuo was to prove Gushan Zhicun’s conjecture!
now what?
Gushan Zhicun's conjecture was not proved, so that's it. What's even more exaggerated is that he came up with another conjecture!
The people at the Cray Institute of Mathematics were almost crying.
Originally, they were too weak to prove the eight conjectures, and now adding another one is just abruptly giving them this "cleaning plan" to increase the difficulty.
…………
Professor Black's complexion was now blue and purple.
He discovered that he really underestimated Cheng Nuo.
Their "geometric conjecture" proved that the group's three-month research results are not worth mentioning 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 the limelight of the report meeting, so after hesitating for a few seconds, he asked Cheng Nuo on the stage, "Mr. Cheng Nuo, your Cheng Nuo The Fuhuan Conjecture does have great research value, but I can’t figure it out. What is the connection between this and the Gushan Zhicun Conjecture you studied?"
"Mr. Black is very good at asking this question." Cheng Nuo said with no change ~EbookFREE.me~, "At first glance, it seems that these two conjectures are not related at all, but what I need to tell you is, There is not only a connection between these two conjectures, but they are also extremely close."
Cheng Nuo swore some formulas on the other half of the blank blackboard.
"I'm afraid you will never be familiar with this formula anymore. When Mr. Wiles was proving Fermat's Last Theorem, he used this series of formulas. Its academic name is called the'Frey's Proposition'."
"Using Frey's proposition and treating it as a bridge, we can perfectly combine the Gushan Zhicun conjecture and the Cheng’s complex ring conjecture. Adding Gushan Zhicun’s conjecture does not hold, and the rational point of the complex number field ellipse in the Cheng’s complex ring conjecture cannot be equal to The number of solutions of finite field equations increases by one. And vice versa!"
A mathematician with a little bald hair in the audience suddenly said, "In other words, if the Gushan Zhicun conjecture is established, the Cheng's complex ring conjecture is established, and the Cheng's complex ring conjecture is established if the Gushan Zhicun conjecture is established?"
Cheng Nuo pointed to the mathematician, "Yes, that's it!"
Wow~!
The audience made an uproar for the first time.
There are some young mathematicians who looked at Cheng Nuo with full admiration.
Without raising his head, Professor Black took out a piece of draft paper and quickly calculated according to the method described by Cheng Nuo, and finally found that the facts were exactly what Cheng Nuo had shown.
The Gushan Zhicun conjecture and the Cheng’s complex ring conjecture are integrated, one is established, and the other will surely be established.
Therefore, Cheng Nuo's work does not require both proofs, only one of them.
…………
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