Wojciech J. Gajda

Abstract:

We shall describe a proof of the fact that if C is a curve over a global field K of positive characteristic, whose Kodaira-Spencer class is non trivial, then C(K^perf) is finite. We shall also give small upper bounds for #C(K^perf). Here K^perf is the maximal purely inseparable algebraic extension of K. The fact that C(K^perf) is finite is a theorem of Minhyong Kim. His argument uses the theory of heights. By contrast, our argument is purely geometric and it quickly leads to simple estimates of the size of C(K^perf).