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Results tagged with nt.number-theory
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user 18850
Prime numbers, diophantine equations, diophantine approximations, analytic or algebraic number theory, arithmetic geometry, Galois theory, transcendental number theory, continued fractions
7
votes
"Nice" definition of discriminant as alluded to in an answer of Qing Liu
I want to mention that there is a published version of Deligne's letter online, namely the famous paper "Le déterminant de la cohomologie". See here:
https://publications.ias.edu/node/404
I am tryin …
3
votes
Accepted
Günter Tamme's course "Arakelov theory and Grothendieck-Riemann-Roch"
Here is a link of Gunter Tamme's course. I take a brief look and it seems centering around proving Gronthendieck-Riemann-Roch using K-theory machinery. I did not see Arakelov theory anywhere. The cour …
- 6,249
1
vote
"Adelic" Arakelov Geometry
This may be more suitable as a long comment. I remember someone asking Soulé current open problems in Arakelov theory during a walk at the summer school (2017) in Grenoble. The adelic intersection the …
- 6,249
26
votes
Accepted
Yitang Zhang's 2007 preprint on Landau–Siegel zeros
This is not an answer regarding the paper, but I think should be helpful. During a recent interview (in Chinese), he commented:
问：前几天我去北京遇到葛立明，他说当时你在做个大问题，快做出来了。所以找你去新罕布什尔大学。
答： 那是关于Siegel零点的工作，我有一篇网 …
- 6,249
2
votes
On explicit examples of the Parshin Construction
If I am not mistaken, you can find such an example in the following lecture notes by Akshay:
http://virtualmath1.stanford.edu/~conrad/mordellsem/Notes/L01.pdf
(to be precise, see the bottom part of pa …
- 6,249
25
votes
2
answers
1k
views
Why it is difficult to define cohomology groups in Arakelov theory?
I have been puzzled by the following Faltings' remark in his paper Calculus on arithemetic surfaces (page 394) for a few months. He says:
If $D$ is a divisor on $X$, we would like to define a hermiti …
- 6,249
6
votes
Theta functions on an elliptic curve and Serre duality
Here is a 'low-brow' approach. One type of the result you are talking about has been written up implicitly in Lang's book Introduction to Arakelov theory. The case for cohomology of the elliptic curv …
- 6,249
1
vote
Why do Chern forms show up in Arakelov geometry?
I apologize for answering late.
I think the 1D case has been discussed multiple times in the forum already. The high dimensional case you suggested was first defined by Bost. See page 63 in below:
Thé …
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