Talks by Shenghao this summer

[胤榜]

I've just uploaded the notes of talks given by Shenghao in Zheda this
summer.
The name of the file is Zheda.pdf.
Someone may be interested.

[Yinbang Lin]

---------- Forwarded message ----------
From: tt <sha...@gmail.com>
Date: 2010/1/15
Subject: Re: Talks by Shenghao this summer
To: 胤榜 <yinba...@gmail.com>


L-functions is a big topic; it's one of the most important branch in
arithmetic geometry/number theory. Do you have any preference on what
kind of L-functions you want to study?

Horizontal ones: For Dedekind zeta functions, Artin L-functions, you
may read the relevant chapters in Lang's ANT to get started.

Vertical ones: For zeta functions of varieties over finite fields,
Hartshorne's Appendix C is the first thing I read, and I found it very
helpful (do the exercises). Also Milne's notes on etale cohomology,
Part II, gives a proof of the Weil conjecture. Grothendieck's article
"Formule de Lefschetz et Rationalite des Fonctions L" is a classical
one on this topic.

Mixed: This means zeta functions of varieties over number fields, like
elliptic curves over rational numbers. This is a very hard topic, and
I know nothing about it. But again, Milne's notes on alg number theory
and elliptic curves (maybe also the one on modular forms) is pretty
helpful (at least to me).

Also I have a summary note on various L-functions. It's not for
publishment, only for personal use.
It has not been finished, and I haven't touched it for a long time
(which means it won't be finished in the near future). I put it in a
secret link at

math.berkeley.edu/~shenghao/zeta.pdf

and hope that it might of some help.

[tt]

Thanks, 胤榜. Now I can post megn again.