Function Fields: Invariants

• The genus
• Exact constant field
• Wronskian orders, gap numbers, ramification divisor and Weierstrass places
• Space of holomorphic differentials
• Intermediate fields of F/k(x)

Additionally for global function fields:

• Places of degree one (in constant field extensions)
• L-polynomial and $\zeta$-function
• Structure of the divisor class group
• p-rank of the divisor class group (separate method) and Hasse-Witt invariant