Unramified Skolem Problems and Unramified Arithmetic Bertini Theorems in Positive Characteristic

In this paper, we prove unramified, positive-characteristic versions of theorems of Rumely and Moret-Bailly that generalized Skolem's classical problems, and unramified, positive-characteristic versions of arithmetic Bertini theorems. We also give several applications of these results.

2000 Mathematics Subject Classification: Primary 11G35; Secondary 11G25, 14G15, 14G25, 14H25

Keywords and Phrases: Skolem's problem, arithmetic Bertini theorem, positive characteristic.

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