11
votes
2answers
1k views

Learning path for the proof of the Weil Conjectures

Assume you are an algebraic geometry advanced student who has mastered Hartshorne's book supplemented on the arithmetic side by the introduction of Lorenzini - "An Invitation to Arithmetic Geometry" ...
3
votes
1answer
440 views

Searching for text for studying Spectral sequence

I'm a graduate student studying algebraic geometry I saw Spectral sequence is important in deformation theory, and many other places in algebraic geometry. Can you recommand me some good text for ...
9
votes
2answers
528 views

Tor sheaves: what do they tell us about geometry

Hi! I fear that I am up to ask a very vague question, but more than an answer I need a suggestion of references I should look up. I need to know everything about Tor sheaves and what do they tell ...
11
votes
9answers
3k views

Good book on Riemann surfaces and Galois theory?

I'm supervising an undergraduate project on Galois theory and covering spaces. I want to have him read about the fact that from a branched cover of a Riemann surface you get an extension of its field ...
15
votes
5answers
4k views

Textbook for Etale Cohomology

What is the best textbook (or book) for studying Etale cohomology?
1
vote
2answers
421 views

Weil bound for characters sums. (reference-request )

Do you know on any good reference on Weil bound for charcter sums over algebraic curves. I prefer reference which assume few previous knowlage.
21
votes
1answer
9k views

If I want to study Jacob Lurie's books “Higher Topoi Theory”, “Derived AG”, what prerequisites should I have?

I've been told that it's important to know modern physics, Differential Geometry and Algebraic Topology for understanding higher structures. Is there any other prerequisite for understanding Lurie's ...
1
vote
1answer
291 views

References For Important Hopf Algebras

Where can I find references that discuss important classes of Infinite Hopf Algebras. By important classes, I mean heavily used in research and of relevance to Hopf Algebraist(s),Physicists, ...
6
votes
2answers
531 views

Book on mixed Hodge structures?

Is there any English textbook about Deligne's mixed Hodge structures? Can you tell me about a reference where they are introduced at least for smooth quasi-projective varieties?
0
votes
1answer
654 views

Abelian Variety and Tangent Bundle ----Reference Request

I am looking for the reference where I can find the proof of the following: If $A$ is an abelian variety then its tangent bundle is trivial.
13
votes
3answers
2k views

A reference for geometric class field theory?

The classic reference of this topic is Serre's Algebraic Groups and Class Fields. However, many parts of this book use Weil's language, which I find quite hard to follow. Is there another reference ...
4
votes
2answers
762 views

Survey of Algebraic K-Theory Since 1980?

I just came across Charles Weibel's Development of Algebraic K-Theory until 1980, and found it really helpful. Is there been anything analogous which surveys the developments in the last 30 years? ...
9
votes
2answers
1k views

Literature on the Springer resolution

Could you suggest me a basic reading list on the Springer resolution? Is there a textbook I can refer to? Or do I need to start with the original paper? Unfortunately googling for "Springer" and ...
72
votes
32answers
42k views

Best Algebraic Geometry text book? (other than Hartshorne)

I think (almost) everyone agrees that Hartshorne's Algebraic Geometry is still the best. Then what might be the 2nd best? It can be a book, preprint, online lecture note, webpage, etc. One suggestion ...