Links
Textbook
Book, Algebraic Curves over Finite Fields, Carlos MorenoOnline notes
Notes, Zeta function, HansenLecture (advanced), Algebraic Geometry, Andreas Gathmann
Book, Algebraic curves, William Fulton
Talk, Integer factoring, Pomerance
Paper, Finding roots of unity in finite fields, Pila
Survey, Hyperelliptic curve cryptography, Scholten & Vercauteren
Survey, Algebraic Geometry Codes, van Lint
History: Riemann, Bourbaki, Weil, Grothendieck (who?).
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The Rising Sea [pdf]
Grothendieck describes two styles in mathematics. First, the hammer and chisel principle is: “put the cutting edge of the chisel against the shell and strike hard. If needed, begin again at many different points until the shell cracks—and you are satisfied”. He says:
"I can illustrate the second approach with the same image of a nut to be opened.
The first analogy that came to my mind is of immersing the nut in some softening liquid, and why not simply water? From time to time you rub so the liquid penetrates better, and otherwise you let time pass. The shell becomes more flexible through weeks and months—when the time is ripe, hand pressure is enough, the shell opens like a perfectly ripened avocado!
A different image came to me a few weeks ago. The unknown thing to be known appeared to me as some stretch of earth or hard marl, resisting penetration. . . the sea advances insensibly in
silence, nothing seems to happen, nothing moves, the water is so far off you hardly hear it. . . yet it finally surrounds the resistant substance."
[Grothendieck 1985–1987, Récoltes et Semailles, pp. 552-3]