Just turned over a new leaf and became a wise and intelligent student

Chapter 378 Fierce battle!

"These are just some scattered superficial things. We are still a long way from a complete solution."

Xu Qingshan stretched lazily.

After a whole night of continuous high-intensity research, he was actually under considerable mental and physical pressure, but compared to Liu Ruochuan, he was more durable.

"Just one night! How much achievement do you expect in just one night? Are you really planning to complete the entire conjecture in one night?"

Liu Ruochuan rubbed his face vigorously. Did he really think that Xu Qingshan was a little too perverted?

If everyone does scientific research like him, then scientist will probably become a high-risk profession in the future.

"It's not even one night. You've done a lot of preparation before. What I've made now may seem like a lot, but it's actually not a breakthrough. What's missing? Or..."

Xu Qingshan looked at Liu Ruchuan, thoughtfully.

Liu Ruochuan felt an inexplicable chill, and he always felt that something unclean was targeting him.

Is it possible that after staying up all night, one will become kidney-deficient and then be contaminated by some dirty things?

Xu Qingshan's eyes became more focused and locked onto Liu Ruochuan.

"How about we continue tonight?"

"what?"

Liu Ruochuan looked incredulous and resistant. He didn't want to endure another night.

"Zhang Ke should be able to handle the summer camp matters tonight. I'll send him a message and we'll use the newly built hangar tonight."

"Really? Spare me!"

Liu Ruochuan let out a shrill, inhuman wail.

"Don't worry, I'll let you go back to sleep for a while and we'll meet in the afternoon."

Xu Qingshan was tidying up the manuscripts on the table. He also tried to clear his mind so that he could recover better.

He will have to go back to Nanchizi later. Huanxi has no classes these two days, so she is staying in Nanchizi to accompany her grandmother. After they are done with their work in a few days and Tong Tong comes back from Tokyo, they will go back to Longjiang together.

That night.

Xu Qingshan pulled the desperate Liu Ruochuan into the laboratory again. Zhang Ke came to help and pulled a few lines to the office to do a simple visualization processing. Zhang Ke helped in the information laboratory, waiting to process the data for test experiments, while Xu Qingshan and Liu Ruochuan continued to fight in the office.

The fluorescent tubes in the office made a slight hum at two o'clock in the morning.

When Xu Qingshan crumpled up the 29th piece of calculation paper and threw it into the wastebasket, Liu Ruochuan was frowning at the module space parameters on the curved screen.

The blue light from the monitor illuminated the wall full of sticky notes. The red marks labeled "B_dR Convergence Vulnerability" looked as hideous as unhealed wounds.

His expression was already slightly dull.

But there was a big devil behind him who kept urging him on, and he couldn't relax. It was as if someone was forcing his brain to hold down the power button. The CPU temperature remained at an extremely high temperature without dropping at all, and the core load was fully utilized.

"The counterexample you mentioned in your notes from the Ecole Normale Supérieure last year."

Xu Qingshan suddenly poked Liu Ruochuan's back with the end of his pen, his eyes gleaming.

“Is it the same structure as the broken spectrum sequence now?”

As he spoke, the tip of his pen hovered three millimeters above the paper, and the ink spread out in tiny dendrites between the fibers of the recycled paper.

Liu Ruochuan took off his glasses and wiped off the mist.

"Back then, it was dealing with the obstacle group of modular p-reduction. Now this." He tapped on the keyboard to call up the simulation data that Zhang Ke had just helped to test. "It's more like the representation theory of the Galois group is eating the cheese of the Hodge structure."

The L function values ​​jumping on the display screen appeared to have a seemingly random but actually fluffy and beautiful pore structure. It was just like someone put a piece of Swiss cheese on the screen, and both of them laughed at the same time.

"Are you sleepy?"

The bored laughter lightened the silent atmosphere, and Xu Qingshan asked Liu Ruchuan.

"It's okay. I was actually quite sleepy just now at around twelve o'clock. But after that time, I felt as if my body was very sleepy, but I was still quite energetic. Now I can't fall asleep even if you ask me to."

Liu Ruochuan complained weakly.

However, no matter how much he complains, he still does the job he is supposed to do.

"I'll go make two cups of coffee. If that doesn't work, I still have some Red Bull left."

Xu Qingshan stood up and twisted his waist twice. Sitting for a long time is indeed not good for the body.

A moment later, he returned with two cups of coffee.

Starting this boring and confusing research again, this scene seemed to be repeated many times. Xu Qingshan's pen tip rustled across the paper, and his sight suddenly froze at the break in the spectral sequence.

It seemed like there was something, but I felt a little flustered and that feeling disappeared.

It seems that even he is a little sleepy, so he should have another sip of coffee.

As he reached for the coffee cup, he caught a glimpse of a bright white dot suspended in the air - like the afterimage of burnt pixels on a display screen, or like the projection of an imaginary singularity on a Riemann surface.

The white dot drifted in three-dimensional space as he rotated the draft paper, and finally stopped at the collapsed position of E32, 1E32, 1.

"check it out."

Xu Qingshan suddenly stood up, held Liu Ruochuan's shoulder, and pointed to a location in the visualization image.

He handed Liu Ruochuan half a piece of hazelnut chocolate.

"What is this? Do you think it will be a breathing hole with a high number?"

Liu Ruochuan stared at that position with wide eyes. The site should not have appeared there originally, and as the data was calculated, the number of sites here gradually increased, forming a configuration matrix.

"I think it's like the snow noise of an old-fashioned TV when it can't receive a signal." Xu Qingshan pointed to a flickering position in the matrix, "but this time the noise contains the codebook for opening p-adic geometry."

The moduli space on the display suddenly distorted, and those discrete L-function values ​​began to slide along the white dot trajectory.

"Remember what I mentioned in my previous paper in MIT? The core obstacle of the Fontaine-Mazur conjecture is that when the Galois representation does not have a geometric origin, the traditional p-adic periodic ring cannot establish an effective correspondence."

Liu Ruochuan suddenly mentioned something that was not very relevant to the data on the screen in front of him.

"Remember, so we need to break through the limitations of Scholze's perfect oid space."

Xu Qingshan looked at the figure, then at Liu Ruchuan, and suddenly turned around and began to search through the pile of draft papers on his desk.

"12 pages, it should be 12 pages, you just told me that a few hours ago!"

Liu Ruochuan felt that his dry blood seemed to be gradually boiling.

He rarely encountered such a situation.

He never thought that doing scientific research with Xu Qingshan could lead to a passionate plot.

Xu Qingshan found page 12.

In the original derivation, the derivation result on page 12 is like a mountain range cut by a sharp blade, abruptly collapsing to zero at E32, 1E32, 1.

The cold wind from the air conditioner in the room brushed across the back of his neck, causing him to shudder.

Xu Qingshan felt goosebumps all over his body.

"When we were working on it, all attempts at p-adic periodic rings failed."

Liu Ruochuan was still sitting in his seat, but when he looked at Xu Qingshan's expression, he knew that there seemed to be nothing wrong with his idea, so he continued.

"You think we have missed some essential structural symmetry." "Last month, when we were walking by the Weiming Lake, you told me that the most elegant proof should be like dewdrops on a lotus leaf."

“It has to maintain a completely spherical shape while also fitting perfectly with the topological structure of the leaf veins.”

Xu Qingshan held up the draft paper in his hand. He shone the light on the paper, as if he wanted to shine through the paper, leaving only the words on it imprinted in the air.

"Now this dewdrop of the Galois group needs to reflect the moonlight of the complex manifold and the p-adic number field at the same time."

The white dot on the screen just now seemed to appear in front of Xu Qingshan's eyes in an instant, and appeared in the air, refracting double phases, casting the shadow of a Klein bottle on the wall next to the frame of Chern Shiing-Shen's manuscript that the school gave to Xu Qingshan.

"found it!"

Xu Qingshan suddenly grabbed the pen, pressed the paper on the table, and pressed hard on the broken part.

“Perhaps we should think about it the other way around—instead of using B_dR to carry the Hodge structure, we should let the Galois group act directly on the differential form itself.”

The vibration of the air-conditioning outlet causes the white dot matrix to undergo a phase change.

The pen tip pierces the paper, and the ink grows along the fiber cracks into a tree-like diagram.

Xu Qingshan drew the differential manifold of the white dot's motion on another piece of paper.

Liu Ruochuan took out two cold vegetable buns from the drawer. They bought them in the cafeteria when they came to the laboratory in the afternoon.

"Just like what the boss of the wonton shop in our cafeteria said? 'The spiciest red oil should be paired with the sweetest fermented glutinous rice.'"

"Just as the most violent noncommutative geometry requires the most gentle logarithmic convergence."

Liu Ruochuan felt that his soul was being led and resonating with Xu Qingshan at this moment. It felt so happy to do scientific research in this way!

That feeling of meeting a soulmate in the mountains and rivers!

Xu Qingshan bit into the bun, and the white dot collapsed into a perfectly symmetrical structure that expanded by prime numbers. The morning light from the window crashed into the house, and dust danced in the beam of light.

"What do you mean? What's next?"

Liu Ruochuan looked at Xu Qingshan with joy, but he was not so excited that he wanted to escape from the office or go off work just because a node was solved. Instead, he stared at Xu Qingshan with sharp eyes.

“I have already thought about the next step.”

Xu Qingshan picked up his coffee cup. He had just stirred the coffee in the cup for a while and it was now swirling.

"Look at the vortex in the cup. Do you think that the two-dimensional projection of the three-dimensional vortex on the liquid surface is isomorphic to the assignment mapping of the p-adic number field?"

Xu Qingshan took out another piece of paper, making it difficult for Liu Ruochuan to tell whether it was drawn by him or printed with coffee, but the pattern traces on it actually reproduced the spherical model of Qp.

Xu Qingshan used a pen to draw the center of the shape.

"If we generalize the value chain of p-adic numbers from the commutative group to the adjoint representation of GLn."

"The local system theory of perfectoid spaces can help us bypass the restrictions on the base domain proposed by Scholze's perfect-oid space and achieve a wider range of geometric applicability."

Liu Ruochuan followed Xu Qingshan's pace and began to organize Xu Qingshan's scattered manuscripts.

"If p-adic periodic rings relate Galois representations to differential equations, we can prove groundbreaking results on the rigidity theorem."

"We introduced a non-Abelian cohomology method to handle Galois representations beyond general linear groups. By constructing Simpson functors, we can correspond any local system to a vector bundle with a filtering structure, breaking through the limitation of 'small representations' in Faltings' early work."

Xu Qingshan did not let Liu Ruochuan handle it alone. The two of them stood by the table, sorting out all the manuscripts from the past few days in an orderly yet chaotic manner, trying to piece together a huge road to truth.

"Define the convergence conditions of the logarithmic differential form, solve the connection extension problem at the boundary of the moduli space, and provide tools for the p-adic study of Shimura varieties."

"Introducing the global trigonometric theorem, revealing the intrinsic symmetry of the Galois representation on the characteristic cluster, etc., Senior, please mark this. This is still worth studying for the understanding of the local-global correspondence in the Langlands program. We should be able to try to move towards the geometric realization of the p-advanced Langlands program."

Victory is at hand.

But if any one of these efforts is wrong, all their previous efforts will have to start over again.

Therefore, these two talented scholars who were placed with extremely high hopes by Capital University, even though they had witnessed many big scenes, were still very nervous in this office with only two people.

Even my breathing became heavy.

As time goes by, the stars in the sky move centimeters by centimeters.

The derivation process was gradually verified, and it was not until the part that needed computer-assisted verification that Xu Qingshan breathed a sigh of relief and said.

"If there are no problems."

"I'll take the data to Zhang Ke for verification!"

Before he could finish his words, Liu Ruochuan jumped up, grabbed the manuscript on the table that recorded various data, and ran straight to the information laboratory.

When he returned to the office, Xu Qingshan was already slumped in his chair, resting.

He didn't say anything, but just sat on the chair and dozed off, waiting for the data to be processed.

Five thirty-two.

The prompt sound of the first verification case passing woke up the voice-controlled lights in the corridor.

At the same time, it also woke up the two people who were already snoring.

"Done?"

"It seems to be done."

The two looked at each other in confusion, and did not seem to be as surprised as they got the results. They stood up and were about to go directly to the hangar of the information laboratory to see Zhang Ke's more comprehensive data, but they found that the office was already in a mess.

It wasn't that a thief broke in, but it was the result of the two of them fighting for two or three nights.

The calculation papers on the floor are dotted with coffee stains. Those brown circles of varying shades are like dewdrops rolling on lotus leaves before dawn.

Zhang Ke's spirit and energy are actually much better than theirs.

He can take a nap and rest for a while, and only needs to get up to help them operate the system when processing data. If there are any errors in the software or hardware, he can repair it on the spot. This can be regarded as a backup guarantee, not real-time monitoring.

But he is also excited to be involved in such important research.

Because this was one of the core purposes of his coming to Xu Qingshan's laboratory.

"How is it? Are the results confirmed to be correct?"

When Liu Ruchuan entered the laboratory, he was much more nervous and out of control than Xu Qingshan. On the contrary, Xu Qingshan looked calm and relaxed.

Zhang Ke nodded.

"Well, the retest was very quick, there is no problem, congratulations Director Liu."

"Is it really done?"

"I did it! I did it! I did it!"

Liu Ruochuan was ecstatic. He finally couldn't suppress his excitement anymore. He turned around and picked up Xu Qingshan, and started shaking him like crazy.

"what!"

The cry did not come from Xu Qingshan, but from Liu Ruchuan.

Xu Qingshan looked helpless.

"Are you OK?"

"I'm fine, I just seem to have a sprained waist."

(End of this chapter)