Scalar extensions of triangulated categories
Pawel Sosna

TL;DR
This paper explores how to extend triangulated categories over a field to larger fields, especially focusing on derived categories of schemes and the behavior of their dimension under such scalar extensions.
Contribution
It provides a method to construct triangulated categories over extended fields and analyzes the dimension change under scalar extensions, particularly for derived categories of smooth projective varieties.
Findings
Constructs triangulated categories over field extensions using base change schemes.
Shows the derived category of the base change scheme corresponds to scalar extension in certain cases.
Analyzes how the dimension of a triangulated category varies with scalar extension.
Abstract
Given a triangulated category over a field and a field extension , we investigate how one can construct a triangulated category over . Our approach produces the derived category of the base change scheme if the category one starts with is the bounded derived category of a smooth projective variety over and the field extension is finite and Galois. We also investigate how the dimension of a triangulated category behaves under scalar extensions.
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