Function Fields: Places

• Zeros and poles of algebraic functions
• Valuation (zero, pole orders) of algebraic functions at places
• Local uniformizer at a place
• Residue class field at a place
• Evaluation of algebraic functions at places
• Expansion of algebraic functions at a place of degree one
• Decomposition of places of k(x) within F/k(x)
• Ramification index, inertia degree
• Bounds on the number of places of degree 1 (global case)
• All places of a prescribed degree (global case)
• Random place of a prescribed degree (global case)