Scholar’s Advanced Technological System

Library activity room.

Faced with half the whiteboard written, the ark retracted the marker pen in its hand and stepped back to look at the whiteboard and said.

“… to solve the problem of the unity of algebra and geometry, it is necessary to strip ‘numbers’ and 'shapes' from the general form of expression and to find commonalities between them in the abstract concept. ”

Standing beside the ark, Chen Yang thought for a moment and suddenly asked.

“The Langlands platform? ”

“It's not just the Langlands platform,” the Ark said earnestly, "and the motive theory, in order to solve this problem, we have to figure out the links between the different homonymous theories. ”

In fact, the problem is a very large one.

The question of the "nexus between different homonymous theories” continues to be subdivided into tens of thousands or even millions of unresolved assumptions, or mathematical propositions.

The outstanding difficulty in algebraic geometry - Hodge's guess - is one of them and the most famous.

Interestingly, however, while so many extremely difficult assumptions stand in the way, the argument motive theory does not need to address them all.

The relationship between the two sides is as if Lehmann and Lehmann were spreading their ideas on the Dillicler function.

“… on the face of it, we are looking at a compound analysis problem, but in fact it is also a question of bias differential equations, algebraic geometry, topology. ”

Looking at the whiteboard in front of us, the ark continues, "Standing at the height of strategy, we need to find a factor in the abstract form of numbers and shapes that can relate to both. Tactically, we can start with the commonalities of the kunneth formula, poincare couples, and so on in a series of homonymous theories, as well as the way I showed you earlier that the L flow forms are applied on a composite plane. ”

As he spoke, Ark Zhou threw his gaze at Chen Yang, who stood beside him.

“I need a theory that can build on the classic theory of one-dimensional up-turn - that is, the success of the Jacobi and Abel clusters theories of curves - to facilitate up-turn of all dimensions. ”

“Based on this theory, we can study the straightening and decomposition in the motive theory, associating H (v) with nonapproximate motive. ”

“I was going to do this part myself, but there are important parts that I deserve to finish. I intend to finalize the unification theory by the end of the year, and I will leave this piece to you. ”

Faced with the request of the Ark, Chen Yang pondered for a while and said.

“Sounds interesting… if I feel right, if I can find this theory, it should be a clue to resolving Hodge's assumptions. ”

The ark nodded down, saying.

“I don't know if I can solve Hodge's speculation, but as a problem of the same kind, its resolution may inspire research into Hodge's speculation. ”

“I know,” Chen Yang nodded, "I will go back and study it carefully... but I can't guarantee that I will be able to solve this problem in a short time. ”

“Never mind, this was not a task that could have been accomplished in a short time, and I was not particularly anxious," the Ark laughed and continued, "but my suggestion was that it would be better to give me an answer within two months. If you're not sure, you better let me know in advance, and I can do this myself. ”

Chen Yang shook his head.

“Two months or less, half a month… should be enough. ”

It was not a self-confident statement, but an affirmation of a near-descriptive tone. The tools used are readily available and even possible ideas for solving the problem have been given by the Ark.

This kind of work does not require subversive thinking and creativity, and it can be solved with effort.

And what he lacks most is perseverance on the road.

Looking at Chen Yang with no expression, Ark nodded and patted his arm.

“Well, I'll leave this to you! ”

……

After Chen Yang left, Ark went back to the library and sat down in his previous position. Turning over the unfinished pile of literature on the table, he continued his earlier research while calculating it on the draft paper with a pen.

From a macro point of view, the evolution of algebraic geometry in recent times can be attributed to two broad directions: the Langlands platform and the Motive theory.

The Lanlander theory, whose spiritual core is the intrinsic linkage of some of the mathematically seemingly irrelevant elements, will not be repeated because many people have heard it.

As for the motive theory, it's less famous than the Langlands programme.

At this moment, he is studying a thesis written by a renowned algebraic geometrist, Professor Voevodsky.

In his paper, this Russian professor from the Princeton Institute of Higher Studies proposed a very interesting category of MOTIVE.

And this is exactly what the Ark needs.

“… motive is the root cause of everything. ”

Read softly with a voice that only you can hear, the ark turns against a line of formulas in the literature, and calculates on the draft paper.

For example, if a number we call n, in decimal, n can be expressed as 100, then it can actually be either 1100100 or 144.

The difference is just whether we choose binary or octal to count it. In fact, whether 1100100 or 144, they all correspond to the number n, which is just a different form of elaboration of n.

Here, n is given a special meaning.

It is both an abstract number and the essence of numbers.

what motive theory studies is a collection of countless n called capitals N.

As the source of all mathematical expressions, N can be mapped to any set of intervals, whether [0, 1] or [0, 9], and all mathematical methods of motive theory apply equally to it.

In fact, this has already addressed the core issue of algebraic geometry, that is, the abstract form of numbers.

This abstract expression is the language of the universe in its true sense, unlike all human languages that are "translated” through different numerical methods.

And if we use mathematics just for everyday life, we may never realize this, and many religions and cultures that give special meaning to numbers, in fact, don't really understand God's language.

One might ask what this could do, in addition to making calculations more cumbersome, but in fact, quite the opposite, is to strip the numbers themselves away from their forms of expression, rather than to help people study the abstract significance behind them.

In addition to laying the theoretical foundations of modern algebraic geometry, Grotendic has another great job to do.

He created a single theory, building a bridge between algebraic geometry and a variety of homogeneous theories.

It's like the main melody of a symphony, from which every particular upper-tune theory can extract its own theme material and play it according to its own tone, tone, or subtle tone, or even original beat.

“… all the theories of harmony together form a geometric object, which can be studied within the framework he opens. ”

“… it turns out. ”

The pupils gradually stained with a hint of excitement and the tip of the pen in the hand of the ark stopped.

A premonition in the middle of nowhere that makes him feel close to the finish line.

This excitement from the depths of the soul is even more pleasant than the first time he has seen the virtual reality world...

……

(With regard to the motive theory, reference is made to Barry Mazur's famous WhatisaMotive, a paper of a scientific nature that is truly eye-opening after reading it.