From child prodigy to chief scientist

Chapter 121 You are indeed right

But when Xu Xiao actually heard Schultz say those words, he still found it hard to suppress his excitement.

"Don't worry, Schultz, I promise I won't tell a third person."

Xu Xiao's mouth was indeed very tight; she would never reveal a secret that she knew but which the village children could turn into a rhyme about the next day.

Seeing Xu Xiao's serious expression, Schultz no longer hesitated and explained his problem.

Then, Schulz spent more than ten minutes explaining in English mixed with German, occasionally gesturing with his fingers to represent various shapes.

"One question that's really bothering me right now is, if we have a projective smooth variety over a complete algebraically closed field of eigenvalue p, does every invertible layer on it have a canonical p-advanced lifting such that the Frobenius action is linear in some sense?"

Given that Schultz only verbally described these issues, and his descriptions were somewhat far-fetched, even the issues themselves were difficult to understand.

However, thanks to her exceptional memory, Xu Xiao was able to clearly recall the entire problem in her mind.

After filling in some of the details in his mind, Xu Xiao basically understood what Schultz wanted to express.

"To summarize, you want to study the linearization problem of Frobenius's linearization on p-adjusted lifting, right?"

"That's right, that's right, you really understand me right away." Schultz nodded happily.

He knew that there must have been some omissions or inaccuracies in his statement just now, and he was already prepared for Xu Xiao to continue asking questions.

However, Xu Xiao's comprehension ability was truly astonishing. After listening to it only once, he understood exactly what he was researching.

Schultz's ideas are indeed very imaginative. Although this is strictly speaking a problem of hybrid eigenvalue arithmetic geometry, it connects several different concepts such as the algebraic geometry of eigenvalue p, formal lifting and p-advance analysis, and Galois representation.

Moreover, in addition to the problem itself, Schultz has also made some progress on this issue.

"I am now trying to find a counterexample for the case of curve (dimX=1), or to prove that it always holds true."

"This problem has a good chance of being solved, but it becomes much more complicated in higher-dimensional cases."

"This seems to involve the deformation theory of form groups, and may require the use of the D-M theory and the framework of crystal cohomology —"

As he finished speaking, Schultz's voice unconsciously softened.

Although his mathematical ability is significantly higher than that of the other team members, he is not yet able to handle these very advanced knowledge well.

That's why he hasn't made any substantial progress on this issue for a long time, and he can only keep it to himself.

Schultz did not mention this issue during the previous coffee corner math exchange event.

He knew that with the other team members' abilities, even if he explained it, they were unlikely to find a good solution, or even understand the problem itself.

In addition, this topic has certain academic value, and he doesn't want too many people to know about it, so as to avoid any unnecessary consequences.

Xu Xiao, on the other hand, was completely different. Schultz knew that Xu Xiao's mathematical ability was superior to his own, and that discussing this issue with him was likely to be fruitful.

Schultz had a good impression of Xu Xiao and believed that he could keep his promise and keep the secret of this topic.

After listening to all of Schultz's ideas, Xu Xiao realized that this was definitely not a problem that could be solved in a short time.

After thinking for a while, Xu Xiao replied, "Okay, Schultz, I'll go back and think about it some more. We can discuss it again tomorrow if we have time."

"No problem, I'll probably be at the coffee corner tomorrow too. Just come find me when you have time."

After parting ways with Schultz, Xu Xiao went downstairs and immediately saw Pan Hong waiting at the bottom of the stairs.

"Pan Hong, have you been waiting long?"

"No, it's fine for me to wander around downstairs."

Pan Hong was also very curious about what Schultz and Xu Xiao had talked about earlier.

But since Schultz didn't intend for her to get involved, Pan Hong wisely refrained from asking Xu Xiao about it.

Back in his hotel room, Xu Xiao put himself into a state of flow and carefully considered the question raised by Schultz.

Based on his own intuition, Xu Xiao felt that Schultz's conjecture was probably correct.

However, to better prove this hypothesis, it is best to rephrase the problem.

Xu Xiao spent the whole night transforming the problem and came up with some research paths that might be effective.

However, verifying each one individually would definitely take a lot of time, and it certainly wouldn't be possible to make a breakthrough in just a few days.

Xu Xiao did not delve any deeper into the research, but in just one night of research, he gained more than a dozen fragments of inspiration, taking another big step closer to completing the entry task.

The next morning, Xu Xiao returned to the coffee corner and, as expected, met Schultz there.

When Xu Xiao arrived, everyone greeted him warmly, showing that he had won everyone over with his performance yesterday.

Schultz knew that Xu Xiao had come to find him, so he took Xu Xiao to the terrace from yesterday once again.

"Xu Xiao, please enlighten me with your views on this issue."

"I wouldn't call it offering advice, but rather sharing my personal perspective. My idea is that it's best to rephrase the original problem first, and then look for suitable tools to solve it."

"Should we rephrase the question? What are the reasons for doing so?"

Schultz was still somewhat puzzled by this, but he humbly asked Xu Xiao for advice.

Xu Xiao naturally had his own considerations, and then patiently explained.

"First, the conditions of your original problem are a bit too strong. This is indeed not a problem when the dimension is 1, but if you directly elevate a single invertible layer to a formal probability, it may be impossible to achieve when the dimension is greater than one."

Listening to Xu Xiao's point of view, Schultz gradually realized that what he said was indeed correct.

In algebraic geometry, since the reversible layer lifting barrier group of the curve (dim=1) is 0, the lifting condition is satisfied.

However, for curved surfaces, high-dimensional clusters, and other similar cases, this group is non-trivial.

In this case, the vast majority of reversible layers would not experience any form improvement at all.

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