God's Crown

Eye problems? "

"???"

"Otherwise, how could it be possible to have a crush on you? Isn't your wife a doctoral student abroad? Can she still have a crush on you, a little policeman? Really?"

"Cut." Gu Wei snorted coldly and turned his head away without speaking.

…………

The time soon came to the time for the graduation defense.

The graduation defense was held in the academic lecture hall, and more than half of the world's top mathematics experts gathered in the academic lecture hall of Stanford University, and even the group sitting on the defense committee seats were big shots.Big guys like Deligne and Langlands are all there.

Before An Yan walked into the academic lecture hall, she was actually not too nervous.But seeing all the bosses below, he suddenly became nervous.

It was Professor Deligne who spoke first, "Ann, don't be nervous, you just need to answer well now."

An Yan took a deep breath, put the prepared materials on the computer and said, "I will now explain the connection between the arithmetic properties and analytical properties of Abelian varieties."

【…

W=W1∪W2∪…∪Ws constitutes a subspace, and we might as well set W□n. Since the subspace of any linear space is the solution subspace of a homogeneous linear equation system, for each i(i=1, 2, ..., s), it is advisable to set Wi as n-1 dimensional subspace (otherwise just expand Wi), and set the linear equations of Wi as solution subspace to be ai1x1+ai2x2+...+ainxn=0, i= 1, 2, ..., s.

From these equations, the polynomial fi(T)=ai1+ai2T+ai3T2+...+ainTn-1, i=1, 2,..., s about the undetermined element T is derived.

For each i, fi(T) has at most n-1 roots, so these polynomials have at most s(n-1) roots. And there are infinitely many elements in F, so there exists t∈F such that fi(t )≠0, that is, ai1+ai2t+ai3t2+…+aintn-1≠0, i=1, 2,…, s.

Let βj=(1, tj, tj2,...,tjn-1)T, j=0, 1, 2,...,n-1, where tj(j=0, 1, 2,...,n-1) satisfies ...

Suppose V=V(f1, f2,...,fk), W=V(g1, g2,...,gl), where k and l are positive integers. Then V∪W=V(fpgq:1≤p≤k , 1≤q≤l). On the one hand, if (a1, a2, ..., an) ∈ V, then all fp are 0 at this point, which implies that all fpgq are at (a1, a2, ..., an ) point is also equal to 0. Therefore V糣(fpgq). Similarly, there is W糣(fpgq). This proves that V∪W糣(fpgq).

On the other hand, take (a1, a2, ..., an) ∈ V(fpgq), if the point is in V, then the proof is complete. If the point is not in V, then for some p0, there is fp0(a1 , a2, ..., an)≠0. And because fp0gq is equal to 1 at (a2, a0, ..., an) for all q, then gq must be 0 at this point, which proves that (a1, a2 ,..., an)∈W. Then we get V(fpgq)∪W.

In summary, V∪W=V(fpgq). Therefore, V∪W is also an affine cluster...

ai1x1+ai2x2+...+ainxn=0, i=1, 2,..., s.

对于每个i，ai1x1+ai2x2+…+ainxn=0表示一个超平面.

Let fi=ai1x1+ai2x2+...+ainxn, then fi=0 (that is, the definition equation of the hyperplane) geometrically represents the affine family Vi defined by the polynomial fi. Since for each subspace, there is a hyperplane containing it , so that for each subspace Wi, there exists an affine cluster Vi containing it, where the values ​​of i are all 1, 2,...,...①]

While explaining the thesis, An Yan looked at everyone's expressions and found that no one seemed to have any doubts.It's just that occasionally someone frowned slightly, not knowing what they were thinking.

Don't you have any doubts at all?An Yan thought so in her heart.

Impossible, no matter how you say it, there should be some people who have some doubts.Looking around, no one raised their hands, and no one looked at him in confusion.

Then everyone here can still understand, so An Yan continued.

After explaining the whole paper, he stared at the people in the academic lecture hall and asked, "I've finished talking about this paper. I don't know if you have any thoughts, or are there any doubts about this paper?"

"How to make h(tj)≠0?" Suddenly someone asked aloud.

An Yan glanced at it, and the person who spoke seemed to be a person from the Neon Country, and his English accent was really hard to understand.An Yan tried her best to listen for a long time before she understood what this man said.

"Simple." An Yan smiled, picked up a pen and began to write on the blackboard, "Obviously g is a homogeneous polynomial of degree s, now let h=g(1,t,...,tn-1)∈F[t] , then h(t) has at most finite roots on F. And there are infinitely many elements in F, so there exists tj∈F(j=0,...,n-1), making h(tj )≠2.②”

"Does anyone have any questions?" An Yan stared at everyone with a smile and looked around.

Everyone, you look at me, and I look at you.Just now An Yan has made it very clear, and re-checked the calculation, even if there are some minor problems, it seems that the flaws are not concealed.It seems inappropriate to raise the question at this time.

"I, I have a problem..." The person who stood up was none other than Wang Yunqi.He looked at the paper and said, "Mr. An Yan, the calculation problem on the seventh page of No. 30 is somewhat unclear. Can you re-check the calculation?"

"Of course." An Yan nodded slightly, took a pen and began to check the calculation on the blackboard, "Is it clear now?"

"There is no problem." Looking at the calculation formula on the blackboard, Wang Yunqi sat down contentedly.

"Next, are there any questions?" The person who spoke this time was not An Yan, but Deligne, "If you have no questions, then Ann's thesis defense is over. It can be raised. If the question is raised after the thesis defense is over, I think this is a way of making things difficult for Ann."

After Deligne finished speaking, no one seemed to speak.

You look at me, I look at you.There seems to be no intention of raising questions between each other.

"Is there really no problem?" Hudson, An Yan's mentor, said this time, frowning slightly, "If everyone doesn't speak, it means that everyone has approved An Yan's calculation results."

In fact, this is no longer a question of whether they recognize it or not. An has indeed calculated the result of the BSD conjecture.Whether they admit it or not, the facts are right in front of them.So, at this time, no one spoke.It is hard to imagine that a 21-year-old boy actually solved such a top-notch Abelian cluster problem as the BSD conjecture.

"I'm counting down to five now. If no one asks a question, it means that An Yan's graduation defense has passed."

"Five..." Deligne counted and looked around.

"Four!" Professor Hudson looked at the academic lecture hall, but still no one stood up to ask questions.

"Three." Professor Langlands raised his eyebrows. Are these guys really all right?Or, have everyone here already understood Ann's paper?

"two……"

"one……"

"If everyone is fine, then..."

"and many more!"