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Regenbogen
Regenbogen
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The Gross-Zagier paper "Heegner points and derivatives of $L$-series", is really computational and hard to plow through. It seems it is futile to read it as such and one must look for a more conceptual understanding.

The more conceptual attempts I know are the following:

$1$. The work of Kolyvagin on Birch-Swinnerton-Dyer conjecture, in which he re-proves part of Gross-Zagier using Euler systems. The problem with this is that some of the original Gross-Zagier is still needed for getting the results on BSD conjecture(if I understand things correctly. Please point out if I am wrong).

$2$. The volume of Darmon and Zhang published by MSRI, in which they attempt a $p$-adic theory. Again this is going away from the original complex analytic case. Again please correct me if I am wrong.

So I am wondering whether anybody published a more conceptual approach to the complex analytic Gross-Zagier theorem. I would be grateful for any references.

The Gross-Zagier paper "Heegner points and derivatives of $L$-series", is really computational and hard to plow through. It seems it is futile to read it as such and one must look for a more conceptual understanding.

The more conceptual attempts I know are the following:

$1$. The work of Kolyvagin on Birch-Swinnerton-Dyer conjecture, in which he re-proves part of Gross-Zagier using Euler systems. The problem with this is that some of the original Gross-Zagier is still needed(if I understand things correctly. Please point out if I am wrong).

$2$. The volume of Darmon and Zhang published by MSRI, in which they attempt a $p$-adic theory. Again this is going away from the original complex analytic case.

So I am wondering whether anybody published a more conceptual approach to the complex analytic Gross-Zagier theorem. I would be grateful for any references.

The Gross-Zagier paper "Heegner points and derivatives of $L$-series", is really computational and hard to plow through. It seems it is futile to read it as such and one must look for a more conceptual understanding.

The more conceptual attempts I know are the following:

$1$. The work of Kolyvagin on Birch-Swinnerton-Dyer conjecture, in which he re-proves part of Gross-Zagier using Euler systems. The problem with this is that some of the original Gross-Zagier is still needed for getting the results on BSD conjecture(if I understand things correctly. Please point out if I am wrong).

$2$. The volume of Darmon and Zhang published by MSRI, in which they attempt a $p$-adic theory. Again this is going away from the original complex analytic case. Again please correct me if I am wrong.

So I am wondering whether anybody published a more conceptual approach to the complex analytic Gross-Zagier theorem. I would be grateful for any references.

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Regenbogen
Regenbogen
  • 1.4k
  • 15
  • 29

Conceptual understanding of the Gross-Zagier theorem.

The Gross-Zagier paper "Heegner points and derivatives of $L$-series", is really computational and hard to plow through. It seems it is futile to read it as such and one must look for a more conceptual understanding.

The more conceptual attempts I know are the following:

$1$. The work of Kolyvagin on Birch-Swinnerton-Dyer conjecture, in which he re-proves part of Gross-Zagier using Euler systems. The problem with this is that some of the original Gross-Zagier is still needed(if I understand things correctly. Please point out if I am wrong).

$2$. The volume of Darmon and Zhang published by MSRI, in which they attempt a $p$-adic theory. Again this is going away from the original complex analytic case.

So I am wondering whether anybody published a more conceptual approach to the complex analytic Gross-Zagier theorem. I would be grateful for any references.