Chapter 457 (1/2)
Chapter 460
interesting things?
Many mathematicians have a slightly puzzled expression.
Cheng Nuo did not mean to interest mathematicians.
He smiles, turns around, picks up a piece of chalk and writes a series of formulas on the small blackboard hanging on the side of the stage.
Let a be a topological ring and a be a continuous group homomorphism of n-dimensional Galois representation over. Then:
homomorphic mapping: GQ → Gln (a)
mapping relationship: e ^ p ^ (n + 1) → E [P ^ n]
reverse limit: TP (E): = lime [P ^ n]
let KP ∞ Q be an extension of the kernel Ker ρ P corresponding to the homomorphic mapping: ρ P: GQ → Gl2 (ZP), that is 】
originally, the mathematicians under the stage were all holding their arms one by one, and their eyes were faintly scanning the lines of formulas, and their looks were ancient.
They just want to see what new tricks Cheng can come up with.
But as time went on, the expressions on mathematicians' faces became more and more calm.
One by one, the body leans forward, and his eyes scrupulously scan the series of formulas written down by Nuo. At the same time, he says something in his mouth, and he doesn't know what he is saying.
【…… The absolute Galois group GQ acts on the Tate module TP (E) such that α ζ = ζ + 1 - | e (FT) |]
in this paper, Cheng Nuo stops writing.
Feeling his chin and thinking for a few seconds, Cheng Nuo heavily drew two lines under the last line of formula.
Dong Dong!
Cheng Nuo knocked on the blackboard and pulled the mathematicians back.
He pointed to the formula that occupied half of the small blackboard and said with a smile, ”this is the interesting thing I said.”
”In a nutshell, if e is an elliptic curve on Q and l is a set of prime numbers with good reduction, then the sequence of integer numbers (α ζ) ζ∈ l can be defined, that is, the DNA sequence of elliptic curve. All ft rational points of E are equal to the number of Solutions + 1!”
Cheng Nuo voice dropped, the group of mathematicians below whispered with each other.
A mathematician raised his hand and asked, ”Mr. Cheng Nuo, is this a new theorem you have deduced?”
Cheng Nuo shook his head. ”No, it's not. Because I haven't figured out a way to prove it. But I've run it on a supercomputer at the Institute and found that this formula holds for 248000
”Because this formula explains the relationship between complex rings, I temporarily named it Cheng's complex ring conjecture!” Cheng Nuo explains with a smile.
Cheng's complex ring conjecture!
Many mathematicians can't help but stare.
It seems hard to believe why such a conjecture suddenly and inexplicably emerges.
As geometric mathematicians, especially among the top ones in the world, they are naturally aware of goods.
This ”Cheng's complex ring conjecture”, they read Cheng Nuo's formula written on the small blackboard several times from the beginning to the end.
Cheng's complex ring conjecture is to use Galois representation method to connect equations on finite field with elliptic curve on complex field.
We should know that complex field geometry has always been a desert area in the field of geometry. Although it is a major direction, it is too complicated to study, and it is too difficult to produce results. No one is willing to study this direction painstakingly.
The complexity of complex field geometry lies in the complexity of representing unit torus.