Scalar extensions of triangulated categories

Abstract

Given a triangulated category over a field $K$ and a field extension $L/K$, we investigate how one can construct a triangulated category over $L$. Our approach produces the derived category of the base change scheme $X_L$ if the category one starts with is the bounded derived category of a smooth projective variety $X$ over $K$ and the field extension is finite and Galois. We also investigate how the dimension of a triangulated category behaves under scalar extensions.

15 pages, comments welcome

References in corpus (3)

• Grothendieck ring of pretriangulated categories
• Linearisations of triangulated categories with respect to finite group actions
• Scalar Extension of Abelian and Tannakian Categories

Cited by in corpus (9)

• Semiorthogonal decompositions and birational geometry of del Pezzo surfaces over arbitrary fields
• Moduli spaces, indecomposable objects and potentials over a finite field
• Scalar extensions of derived categories and non-Fourier-Mukai functors
• The toric Frobenius morphism and a conjecture of Orlov
• Rank 2 local systems and abelian varieties
• Rank 2 Local Systems, Barsotti-Tate Groups, and Shimura Curves
• High Frobenius pushforwards generate the bounded derived category
• Commuting matrices and volumes of linear stacks
• Scalar extensions of categorical resolutions of singularities