论文标题
Kontsevich-Zagier积分操作规则和Hrushovski-Kazhdan风格的动机集成的A $ P $ -ADIC变体
A $p$-adic variant of Kontsevich-Zagier integral operation rules and of Hrushovski-Kazhdan style motivic integration
论文作者
论文摘要
我们证明，如果$ \ mathbb {q} _p^n $的两个半代数子集具有相同的$ p $ -Adic措施，那么只能使用一些基本的积分转换规则来推导此平等。一方面，这可以将其视为对肯特维奇·扎吉尔（Kontsevich-Zagier）在真实中提出的问题的$ p $ addic类似物的积极答案（尽管真实问题中的问题很难）。另一方面，我们的结果也可以被认为是指出超过$ \ mathbb {q} _p $，通用动机集成（从hrushovski-kazhdan的意义上）只是$ p $ - addic的集成。
We prove that if two semi-algebraic subsets of $\mathbb{Q}_p^n$ have the same $p$-adic measure, then this equality can already be deduced using only some basic integral transformation rules. On the one hand, this can be considered as a positive answer to a $p$-adic analogue of a question asked by Kontsevich-Zagier in the reals (though the question in the reals is much harder). On the other hand, our result can also be considered as stating that over $\mathbb{Q}_p$, universal motivic integration (in the sense of Hrushovski-Kazhdan) is just $p$-adic integration.
