A Hermite-Minkowski type theorem of varieties over finite fields

2015/12/08 by Toshiro Hiranouchi, Hiranouchi, Toshiro
Mathematics · #FOS: Mathematics #Number Theory (math.NT) #math.NT

paper · pdf · doi:10.48550/arxiv.1512.02348

arxiv created 2016/12/09 · arxiv updated 2016/12/12

Abstract

As an application of P. Delgine's theorem (Esnault and Kerz in Acta Math. Vietnam. 37:531-562, 2012) on a finiteness of l-adic sheaves on a variety over a finite field, we show the finiteness of étale coverings of such a variety with given degree whose ramification bounded along an effective Cartier divisor. This can be thought of a higher dimensional analogue of the classical Hermite-Minkowski theorem.

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