论文标题
带有免费操作员的代数类别中的Weil Descent函子
The Weil descent functor in the category of algebras with free operators
论文作者
论文摘要
我们证明存在$ \ Mathcal {d} $ - 代数的类别中的Weil下降或Weil限制的版本。该类别的对象是$ k $ -Algebras $ r $配备了同构$ e \ colon r \ r \ otimes_k \ Mathcal {d} $，用于某些固定字段$ k $和有限型 - 二型$ k $ -k $ -Algebra $ \ algebra $ \ Mathcal {d} $。我们在对所谓相关的内态性的温和假设下进行此操作。特别是，这产生了Weil Descent函数在差异类别中的存在，据我们所知，该类别不会出现在其他地方。
We prove that there exists a version of Weil descent, or Weil restriction, in the category of $\mathcal{D}$-algebras. The objects of this category are $k$-algebras $R$ equipped with a homomorphism $e \colon R \to R \otimes_k \mathcal{D}$ for some fixed field $k$ and finite-dimensional $k$-algebra $\mathcal{D}$. We do this under a mild assumption on the so-called associated endomorphisms. In particular, this yields the existence of the Weil descent functor in the category of difference algebras, which, to our knowledge, does not appear elsewhere.
