Formality of $\mathbb{P}$-objects

TL;DR

This paper proves that certain algebraic objects called $P$-objects have formal derived endomorphism algebras, making their generated categories invariant under ambient changes, with implications for the structure sheaf of smooth projective varieties.

Contribution

It establishes the formality of derived endomorphism algebras for $P$-objects and simple configurations, and shows the category generated by a structure sheaf depends only on cohomology algebra.

Findings

$P$-objects have formal derived endomorphism algebras

Categories generated by such objects are ambient-independent

Category generated by a structure sheaf depends only on cohomology algebra

Abstract

We show that a $\mathbb{P}$-object and simple configurations of $\mathbb{P}$-objects have a formal derived endomorphism algebra. Hence the triangulated category (classically) generated by such objects is independent of the ambient triangulated category. We also observe that the category generated by the structure sheaf of a smooth projective variety over the complex numbers only depends on its graded cohomology algebra.