Function Field

Results named in Tau Ceti's TauCeti.FieldTheory.FunctionField modules and in no roadmap's section, as Tau Ceti has them at commit ace60277.

The Artin--Schreier genus… to The tame different theorem…

• The Artin--Schreier genus formula, cross-multiplied for a possible constant-field extension
• Castelnuovo's inequality (Stichtenoth, Theorem 3.11.3)
• Clifford's theorem
• Dedekind's different theorem, first part (Stichtenoth, Theorem 3.5.1(a))
• The Eisenstein criterion (Stichtenoth, Proposition 3.1.15)
• The fundamental identity
• The fundamental inequality (Stichtenoth, Theorem 3.1.11)
• The Galois correspondence for the inertia field
• Hilbert's different formula
• The Hurwitz bound (Stichtenoth, Exercise 3.18)
• Kummer's theorem (Stichtenoth, Corollary 3.3.8)
• Kummer's theorem sees one factor per place
• The relative degree bound of Kummer's theorem (Stichtenoth, Theorem 3.3.7)
• The residue action, on residues (Stichtenoth, Theorem 3.8.2)
• The residue theorem for k(x) (Stichtenoth, Corollary 4.3.3, for k(x))
• The residue theorem for k(x) over an algebraically closed field (Stichtenoth, Corollary 4.3.3, for k(x))
• Riemann's inequality (Stichtenoth, Corollary 3.11.4)
• Stichtenoth's transformation formula
• Strong approximation (Stichtenoth, Theorem 1.6.5)
• The tame different theorem fails at infinity

The weak approximation theorem to Weierstrass gap theorem…

• The weak approximation theorem
• Weierstrass gap theorem (Stichtenoth, Theorem 1.6.8)

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