Although there surely is plenty of references on MSE about algebraic curves, my need are very specific and so I will open this topic anyway.
I follow this year a course on (hyper)elliptic curves cryptography. The teacher is not very accurate and there is no lecture notes (aside from beamer slides). Things are not always well defined, results are thrown at us often without proofs and without references to them. Well, it becomes difficult to follow the course and to have a good comprehension of the subject.
I would then want some references about
- algebraic curves in general,
- the specificity of (hyper)elliptic curves over (algebraic closure of) finite fields.
I'm a graduate student in mathematics, so I have a strong background in pure mathematics. However, I did very little algebraic geometry : more specifically I followed an introduction to scheme theory, and an introduction to algebraic groups and I did a lot of commutative algebra. But I'm very not familiar with divisors, Picard groups, or the algebraic Riemann-Roch theorem. I heard about Fulton's Algebraic curves and I will take a look at it. Any other references ?