Uniqueness of dg-lifts via restriction to injective objects

TL;DR

This paper proves a unique reconstruction method for dg-lifts of derived functors in algebraic geometry, using restrictions to injective objects, applicable to schemes and derived categories.

Contribution

It introduces a purely algebraic-categorical technique to establish the uniqueness of dg-lifts via restrictions to injective objects.

Findings

Uniqueness of dg-lifts for derived pushforward and pullback functors.

Applicable to both unbounded and bounded below derived categories.

Reconstruction from injective objects is effective and algebraic.

Abstract

We prove a uniqueness result of dg-lifts for the derived pushforward and pullback functors of a flat morphism between separated Noetherian schemes, between the unbounded or bounded below derived categories of quasi-coherent sheaves. The technique is purely algebraic-categorical and involves reconstructing dg-lifts uniquely from their restrictions to the subcategories of injective objects.