For primes $p$, we investigate an $\mathbb{F}_p$-version of simplicial volume and compare these invariants with their siblings over other coefficient rings. We will also consider the associated gradient invariants, obtained by stabilisation along finite coverings. Throughout, we will discuss the relation between such simplicial volumes and Betti numbers.

中文翻译：

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$$\mathbb {F}_p$$Fp 系数的单纯体积

对于素数 $p$，我们研究了单纯体积的 $\mathbb{F}_p$ 版本，并将这些不变量与其他系数环上的兄弟变量进行比较。我们还将考虑相关的梯度不变量，通过沿有限覆盖的稳定性获得。在整个过程中，我们将讨论这种单纯体积与 Betti 数之间的关系。