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Formality of $\mathbb{P}$-objects

Part of: Homological methods (Co)homology theory Abelian categories

Published online by Cambridge University Press:  03 May 2019

Andreas Hochenegger  and
Andreas Krug
Andreas Hochenegger
Affiliation:
Dipartimento di Matematica ‘Federigo Enriques’, Università degli Studi di Milano, via Cesare Saldini 50, 20133 Milano, Italy email [email protected]
Andreas Krug
Affiliation:
FB 12 Mathematik und Informatik, Philipps-Universität Marburg, Hans-Meerwein-Straße 6, 35032 Marburg, Germany email [email protected]
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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.

Keywords

ℙ-objectformality of endomorphism algebrastriangulated category

MSC classification

Primary: 18E30: Derived categories, triangulated categories 14F05: Sheaves, derived categories of sheaves and related constructions 16E40: (Co)homology of rings and algebras (e.g. Hochschild, cyclic, dihedral, etc.)
Type
Research Article
Information
Compositio Mathematica , Volume 155 , Issue 5 , May 2019 , pp. 973 - 994
Copyright
© The Authors 2019 

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