P-极小结构中的微分与p-adic局部单调性定理
Differentiation in P-minimal structures and a p-adic Local Monotonicity Theorem
摘要：
我们证明了一个p-adic，局部版本的单调性定理的P-极小结构。这个定理的存在性最初是由Haskell和Macpherson证明的。我们通过考虑一阶严格导数来处理这个问题。特别地，我们证明了对于一类广泛的P-极小结构，可定义函数f：K -> K是几乎处处严格可微的，并且满足局部雅可比性质.
英文摘要：
We prove a p-adic, local version of the Monotonicity Theorem for P-minimal structures. The existence of such a theorem was originally conjectured by Haskell and Macpherson. We approach the problem by considering the first order strict derivative. In particular, we show that, for a wide class of P-minimal structures, the definable functions f : K -> K are almost everywhere strictly differentiable and satisfy the Local Jacobian Property.
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