Submission date: 19 August 2022

Abstract:

We prove that there exists a version of Weil descent, or Weil restriction, in the category of D-algebras. The objects of this category are k-algebras R equipped with a homomorphism e : → R ⊗_k D for some fixed field k and finite-dimensional k-algebra 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.

Mathematics Subject Classification: 12H05, 12H10, 14A99

Keywords and phrases: Weil descent, left adjoints, differential algebra, difference algebra, fields with operators

Full text arXiv 2207.09546: pdf, ps.