Wind from Rio, III

代数幾何講演会

“A tower of curves over cubic finite fields and the bound of Th.Zink. ”

Arnaldo Leite Pinto Garcia (IMPA, Brazil)

講演要旨: The search for explicit towers of curves (or of function fields) over finite fields received many attention from mathematicians since Tsfasman-Vladut-Zink showed that, using towers and a coding construction due to Goppa, one can construct infinite sequences of linear codes over finite fields with limit parameters above the so-called Gilbert-Varshamov bound. We know of very good towers over finite fields with square cardinalities; many of them attain the Drinfeld-Vladut bound. The aim of this talk is to present a new tower over finite fields with cubic cardinalities having a very good limit for the ratios of number of rational points over the genus. The limit is good enough for getting also here an improvement on the Gilbert-Varshamov bound. The new feature of this tower is that all the maps in the tower (or all the field extensions in the tower) are nonGalois.