On Maximal Curves

✍ Scribed by Rainer Fuhrmann; Arnaldo Garcia; Fernando Torres

• Publisher: Elsevier Science
• Year: 1997
• Tongue: English
• Weight: 407 KB
• Volume: 67
• Category: Article
• ISSN: 0022-314X
• DOI: 10.1006/jnth.1997.2148

✦ Synopsis

We study arithmetical and geometrical properties of maximal curves, that is, curves defined over the finite field F q 2 whose number of F q 2 -rational points reaches the Hasse Weil upper bound. Under a hypothesis on non-gaps at a rational point, we prove that maximal curves are F q 2 -isomorphic to y q +y=x m , for some m # Z + . As a consequence we show that a maximal curve of genus g=(q&1) 2 Â4 is F q 2-isomorphic to the curve y q +y=x (q+1)Â2 .