Chen Zhou said hello to Liu Maosheng and Zeng Zigu here, and followed Deligne to a nearby café.

In the café.

When the waiter asked what he needed, Chen Zhou only ordered a glass of boiled water.

To be honest, Chen Zhou doesn't like coffee very much, he really can't get used to it.

In contrast, plain water is the real mass drink.

Looking at the young man opposite, Deligne asked softly, "Do you know why I'm looking for you?"

Chen Zhou thought for a while and said uncertainly: "On the topic of standard conjecture?"

Deligne nodded: "It's related to the teacher's subject." ”

After receiving an affirmative answer, Chen Zhou was even more confused.

I can't seem to help him solve the standard conjecture, right?

And I don't have any research experience with standard conjectures, so I can't help much.

Could it be that Professor Deligne thinks so highly of himself that he thinks that he will be able to solve the subject he is studying, so he is trying to persuade himself to study the standard conjecture?

I'm not kidding myself, is it?

Chen Zhou asked himself, he was definitely not as good as the old man in front of him.

The problem of standard conjecture is not only in the present, but also in the future.

At least now, he is far from being able to solve this problem.

Deligne had been observing Chen Zhou, and after noticing Chen Zhou's puzzled expression, he didn't immediately explain.

Instead, he took a sip of coffee and told a story without hurrying.

"I remember that as early as 1959, Dworker proved the first Wey conjecture using the p-entry method, that is, the ζ function of the finite body dissolution is a rational function. ”

"Later in 1964, my teacher Grothendieck, proved that Wey's conjecture was more general, and introduced his 'formal system of hexanomial operations'. ”

Later, the teacher proved the second Wey conjecture, which is the ζ function of the solution, satisfying a functional equation. ”

It was also during the 60s of the last century that finding a way to prove the final Wey conjecture became the main source of inspiration for the teacher's research and his obsession. ”

"The 'standard conjecture' was constructed and proposed during this time period. The teacher always believed that if these standard conjectures could be proved, the entire Wey conjecture could be proved. And, mired in this ......"

Listening to Deligne's narration, the puzzled expression on Chen Zhou's face had gradually disappeared.

He vaguely guessed the reason for Deligne's unique opening remarks in the lecture.

As Drinje said, the standard conjecture was Grothendieck's last regret.

It is also the regret of Deligne, who bypassed the standard conjecture and proved the Wey conjecture.

And the reason for this regret, Deligne is telling Chen Zhou.

"Because I was deeply influenced by my teacher, I also focused on the standard conjecture at the beginning of my research on the Wey conjecture. ”

"It wasn't until later that I saw Professor Lanjin's paper, which discussed the classical modular form theory that the teacher didn't know. ”

And this key concept successfully helped me bypass the standard conjecture and proved Wey's final conjecture. ”

This is why some mathematicians later said that in order to prove the final Wey conjecture, more classical material was needed, and this was Grothendieck's blind spot. ”

"But in fact, this is the biggest misconception about teachers!"

There was something strange in Deligne's voice, so much so that his voice trembled slightly.

At this moment, Chen Zhou is obviously a qualified listener.

At the same time, he is also trying to understand this sentiment of Deligne.

Deligne's words also made Chen Zhou confirm his guess.

In today's lecture, Deligne really had that opening remark because of Grothendieck.

It was also two years after Grothendieck's death that Deligne took advantage of this occasion to vent a certain emotion.

It's just that what Chen Zhou doesn't understand is, why two years later?

Also, why did the other party say these things to himself?

Deligne paused for a moment, curbing his emotions a little before continuing: "In the teacher's mind, the Wey conjecture is important because it is the tip of the iceberg, reflecting the basic mathematical structure that he wants to discover and develop. ”

"If we can prove the standard conjecture, we can reveal this structure more deeply. That is, the Wayy conjecture should serve the standard conjecture. ”

"In the process of proving the Wey conjecture, there must not be a circumvention of the standard conjecture!"

"If I use Motive's theory, the teacher will be very interested. Because this means that there is a new development in the standard conjecture. ”

"But I spared the tip of the iceberg, completely detached from standard conjecture......"

Speaking of this, Deligne sighed softly: "Because of this, the teacher is not too interested in my ingenious proof. ”

Chen Zhou didn't know how to comfort the math master.

But Chen Zhou heard the cause and effect clearly.

Chen Zhou felt that Deligne's lecture today was probably the first step to make up for Grothendieck's regrets and his own regrets.

After a moment of silence, Deligne picked up his coffee and took another sip.

Looking at the young man opposite, Deligne suddenly said, "Do you have any thoughts on today's lecture?"

Chen Zhou thought for a while and said: "Milno's conjecture, I think these new research results should be able to promote the solution of Milno's conjecture, and do not provide the key to the solution of many propositions." ”

The Mirno conjecture is a proposition that links the theory of cohomology with the theory of algebraic K-theory, and also involves the theory of quadratic types, which is one of the most important problems in algebraic K-theory in the past two or three decades.

More importantly, if the Milno conjecture is resolved.

Then, this breakthrough in mathematical theory will take an extremely crucial first step in solving the Bellingson-Richtenbaum conjecture and the Bloch-Kato conjecture.

These mathematical conjectures are the basic "results" of the establishment of special algebraic diversity obtained by Bellingson, Bloch, Richtenbaum and others over the years when they studied the standard conjectures.

The reason why this result is in double quotation marks is because these basic propositions are just conjectures.

But now, Drinne's research seems to have made it possible for these conjectures to become theorems.

It also made it possible for Grothendieck's standard conjecture to be further developed.

Although Chen Zhou's answer is not so clear.

If you want ordinary people to listen, you may not know what Chen Zhou is talking about at all.

However, when Deligne heard Chen Zhou's answer, his eyes suddenly lit up.

Looking at Chen Zhou's eyes, he also became a little subtle.

"I originally thought that your research field had been limited to analytic number theory, and your understanding of algebraic geometry was not deep enough. But your answer exceeded my expectations. ”

Deligne unabashedly praised Chen Zhou.

Chen Zhou explained: "There is probably no mathematician who is not interested in such a difficult problem as the standard conjecture. What's more, my mentor was Professor Atin of algebraic geometry. ”

Deligne smiled and nodded: "I almost forgot, your graduate supervisor is Michael Artin." ”

After a pause, Deligne asked Chen Zhou: "Since you also said that you are interested in standard conjecture, have you ever thought about turning around and studying this topic?"

Chen Zhou was stunned for a moment when asked, is this the ultimate goal of finding himself?

However, without waiting for Chen Zhou to answer, Deligne himself said first: "I am very optimistic about your research in this area, and I also want to believe that you can achieve the same achievements as analytic number theory." ”

"Besides, I don't know if you are interested in my research group, come and study with me?"

Chen Zhou looked at Deligne with a strange expression, what does this little old man mean?

First told himself a story, then asked himself what he wanted to listen to, and now he directly invited himself to join his research group.

Is this the legendary technique of throwing bricks and attracting people to join the gang?

"That...... Professor Deligne......" Chen Zhou said hesitantly, "I think that I may not be suitable for the study of standard conjectures at present...... So, thank you for your kindness......"

When Deligne heard this, he just smiled and said: "It's okay, the solution of the standard conjecture will not take a year or two, when you are ready, we will study it together, and it is okay." ”

Chen Zhou was speechless for a moment, this is too ......

But then, Deligne continued: "This invitation does not mean that I am the main one, or that you have come to serve my research group. The two of us will be an equal partnership. ”

Chen Zhou glanced up at Deligne, the meaning of these words, or the weight of these words, was a little too heavy.

Although Chen Zhou has just won the Cole Number Theory Prize, he has won the highest honor in the field of number theory.

But in front of Deligne, he was just a toddler just starting out in the world of mathematics.

In any sense, he does not have the same level as Deligne as a research collaborator on the subject of the Standard Conjecture.

It's not that Chen Zhou's ability is completely insufficient.

Just because the other party is Deligne.

Keenly aware of Chen Zhou's changes, Deligne said softly: "My teacher encountered great technical difficulties when studying standard conjectures and developing Motive theory. ”

"I'm sure you've learned from my lectures. The most serious problem in the study of standard conjectures is that in order to achieve the idea of the teacher's Motive theory, it is necessary to construct enough algebraic closed chains. ”

But unfortunately, even though he consumed a lot of mind and wisdom, he still couldn't find the Motive theory in his heart. ”

"And since then, no one has ever succeeded in ......"

Chen Zhou didn't react for a while, he didn't understand why Deligne said such a thing again.

Chen Zhou hesitated and said, "Professor Deligne, your research is getting closer to this theory, isn't it?"

Deligne shook his head slightly: "Although the mathematical community is not yet convinced of my research results, I myself understand that this is just the beginning, and it is not even close to this theory. ”

Hearing Deligne's words, Chen Zhou was silent.

He felt that Deligne was a little pessimistic.

In fact, the importance of this research result is gradually becoming prominent.

Just as Chen Zhou just thought, the series of propositions portrayed by this achievement are not unimportant.

Deligne glanced at Chen Zhou, who didn't speak, picked up the coffee that had been cold, and put it down again.

"I've always felt that it may be because of the obsession with Motive's theory and the study of the standard conjecture that the teacher has not been able to solve the Weiyi conjecture. ”

"But the Wayy conjecture was solved by me in a clever way......"

Chen Zhou obviously heard a hint of pathos from Deligne's voice.

Pursing his lips, Chen Zhou said loudly: "But it is undeniable that the proof of Wei Yi's conjecture is one of the greatest achievements of algebraic geometry in recent decades. ”

Deligne shook his head: "If I hadn't bypassed the standard conjecture, I might have been able to accept it." But now, all I have left is regret......"

After a pause, Deligne looked at Chen Zhou and finally said the truest thoughts in his heart.

"Chen Zhou, I know it may be presumptuous to say this, but I have to give a reasonable explanation for what I just said. ”

Chen Zhou nodded slightly, and Deligne continued: "The research of the standard conjecture should require mathematicians to keep trying and finally complete. ”

"Just like Fermat's theorem, it took hundreds of years of trying and finally being proved by Professor Wiles. Standard conjecture, as it should be. ”

"As the originator of the standard conjecture, my teacher Grothendieck was the mathematician who originally studied the standard conjecture. Unfortunately, he was not able to finally solve this problem, which may be of the future. ”

When it comes to the future, there is a kind of expectation in Deligne's eyes.

"I should have been the closest to my teacher's ideas in the study of the standard conjecture, but ......alas," continues Déligne, "to make up for this regret, I have been obsessed with the study of the standard conjecture in recent years, and have achieved the results known to you." ”

"However, in the study of the standard conjecture, I know that the solution of this conjecture will not be in me. I'm just a paving guide for future generations. ”

"So, I hope you can, after me, not give up on the study of standard conjectures......"

After Deligne's words were finished, Chen Zhou finally understood.

Deligne: This is looking for the "inheritor" of the standard conjecture.

Chen Zhou felt that it was probably the meaning of the inheritor.

From Grothendieck to Deligne, it's the same lineage.

But after Deligne, he himself did not have a suitable "inheritor".

So, he found Chen Zhou.

Of course, Chen Zhou feels that Deligne's obsession with standard conjectures mostly comes from his heart wanting to make up for his regrets.

And this heart, the feelings contained in it, are all the teacher-student relationship between him and Grothendieck.

From this conversation, Chen Zhou finally understood the feelings of mathematicians.

From the beginning of mathematics to the end of mathematics.

To be honest, Deligne's request was not too difficult for Chen Zhou.

On the road of mathematics, Chen Zhou, who is "determined" to build his own mathematical edifice, must be unable to avoid the standard conjecture, which is the most important problem in the field of algebraic geometry.

However, Chen Zhou had to figure out one thing.

That is, why him?

In contrast, Schultz, a supergenius in the field of algebraic geometry.

Shouldn't it be more appropriate?