After that, the rest fell into place.

It's like using an ax to chop down a big tree.

Although this tree is unimaginably huge, you can still use it to chop it down bit by bit as long as you have enough time.

Using algebraic variety and group mapping tools to complete the Hodge conjecture is like using an ax to chop down a towering tree.

Perhaps one day in the future, the mathematical community will be able to find a more efficient tool like a 'chainsaw', but now, the importance and sharpness of this ax cannot be doubted.

It successfully opened the invisible shackles that Hodge guessed, and revealed the door to the new world in front of everyone's eyes.

.....

On the other side, in the front row of the lecture hall, among the several rows of seats that had been arranged in advance, an old man looked at the young man on the stage with cloudy but profound eyes.

On both sides of the old man were two other slightly younger men. One was Professor Pierre Deligne from the Institute for Advanced Study in Princeton.

The other one is Professor Gerd Faltings of the Max Planck Institute of Mathematics.

With two of the world's top math masters by his side, one can see that the old man in the middle has an extraordinary status.

And in fact, so is he.

Just because this old man's name is Jean-Pierre Serre.

The youngest winner of the Fields Medal in history, the first winner of the Abel Prize, the Wolf Prize in Mathematics, and the first genius mathematician to win three grand slam prizes in the history of mathematics.

After the death of Pope Grothendieck in 2014, this old man can be said to be the greatest scholar in the world of mathematics today.

He has profound research in pure mathematics such as topology, algebraic geometry, and number theory. Even Faltings, who is now vaguely known as the first person, is like a student in front of him.

However, Serge is now ninety-one years old and has already retired to enjoy his old age.

In fact, the Institute for Advanced Study in Princeton did not send an invitation letter to Serge. After all, you have to consider whether his age and physical condition can withstand the hardship.

But unexpectedly, after learning the news, Serge was determined to come over in person, no matter how much the people around him tried to persuade him, it was of no use.

Staring at the young man on the stage who was explaining seriously, Serge's eyes were hazy, as if time had returned to seventy years ago, when he was still a student attending Professor Hilbert's lecture.

That majestic figure is so similar to the young man today.

...

At the same time, with Xu Chuan's explanation, the proof process of Hodge's conjecture entered the core final stage.

On the podium, Xu Chuan turned over a page of ppt manuscript: "...Based on mapping tr, restriction mapping and poincar′e, the duality theorem is all compatible with the action of gal(k/k), so gal(k/k

) also has trivial effects on the cohomology class defined by y."

When the final moment came, the entire auditorium fell silent, and you could hear a pin drop.

Some of the whispered discussions that had arisen over algebraic varieties and group mapping tools disappeared at this moment. Even the scholars who could not understand the paper report at this moment felt a strange feeling in their hearts.

As a result, all the audience couldn't help but hold their breath and stared closely at the curtain on the stage.

On it, there are the final steps to prove the Hodge conjecture.

As the last step came, Xu Chuan moved his eyes away from the projection screen and looked at the audience in the audience.

After taking a deep breath, he said calmly: "When i ≤ n/2, the quadratic form x→(?1)il?r?2i( on ai (x)n ker (l?n?2i 1)

x.x) is positive definite..."

"From this, it can be concluded that on non-singular complex projective algebraic varieties, any Hodge class is a rational linear combination of algebraic closed-chain classes."

"That is, the Hodge conjecture is established!"

When the last words fell, the Alexandria Auditorium was instantly filled with thunderous applause.

After Lefschetz proved that Hodge's conjecture was correct in low-dimensional space in 1924, it has gone through nearly a hundred years of ups and downs. Regardless of the final conclusion, at this moment, the genius boy standing on the stage

, using his own theory to end a century-old problem.

Moreover, it conquered mathematicians from all over the world!
Chapter completed!