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1 results

  • On Subfields of the Hermitian Function Field

  • Arnaldo Garcia, Henning Stichtenoth, Chao-Ping Xing
  • Journal:
    Compositio Mathematica / Volume 120 / Issue 2 / January 2000
    Published online by Cambridge University Press:
    04 December 2007, pp. 137-170
    Print publication:
    January 2000
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  • The Hermitian function field H= K(x,y) is defined by the equation yq+y=xq +1 (q being a power of the characteristic of K). Over K=${\mirrored F}$q2 it is a maximal function field; i.e. the number N(H) of ${\mirrored F}$q2-rational places attains the Hasse–Weil upper boundN(H)=q2+1+2g(H)·q. All subfields K[subnE ] E⊆H are also maximal. In this paper we construct a large number of nonrational subfields E⊆H, by considering the fixed fields H$^{\mathcal G}$ under certain groups ${\mathcal G}$ of automorphisms of H/K. Thus we obtain many integers g[ges ]0 that occur as the genus of some maximal function field over ${\mirrored F}$q2.