On the Deuring-Shafarevich Formula

Daisuke SHIOMI

doi:10.3836/tjm/1327931387

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Home > Journals > Tokyo J. Math. > Volume 34 > Issue 2 > Article

December 2011 On the Deuring-Shafarevich Formula

Daisuke SHIOMI

Tokyo J. Math. 34(2): 313-318 (December 2011). DOI: 10.3836/tjm/1327931387

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Abstract

In this paper, we will give a new proof of the Deuring-Shafarevich formula, which asserts a relation between the $p$-ranks of Jacobi varieties. We analyze the zeta functions of global function fields to prove the formula, without using tools of the algebraic geometry.