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Proceedings of the American Mathematical Society Series B

Published by the American Mathematical Society since 2014, this gold open access, electronic-only journal is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 2330-1511

The 2024 MCQ for Proceedings of the American Mathematical Society Series B is 0.95.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

A short computation of the Rouquier dimension for a cycle of projective lines
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by Andrew Hanlon and Jeff Hicks;
Proc. Amer. Math. Soc. Ser. B 11 (2024), 653-663
DOI: https://doi.org/10.1090/bproc/252
Published electronically: December 11, 2024

Abstract:

Given a dg category $\mathcal C$, we introduce a new class of objects (weakly product bimodules) in $\mathcal C^{op}\otimes \mathcal C$ generalizing product bimodules. We show that the minimal generation time of the diagonal by weakly product bimodules provides an upper bound for the Rouquier dimension of $\mathcal C$. As an application, we give a purely algebro-geometric proof of a result of Burban and Drozd that the Rouquier dimension of the derived category of coherent sheaves on an $n$-cycle of projective lines is one. Our approach explicitly gives the generator realizing the minimal generation time.
References
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Bibliographic Information
  • Andrew Hanlon
  • Affiliation: Department of Mathematics, Dartmouth College, Hanover, New Hampshire 03755
  • MR Author ID: 1079907
  • Email: andrew.hanlon@dartmouth.edu
  • Jeff Hicks
  • Affiliation: School of Mathematics, The University of Edinburgh, Old College, South Bridge, Edinburgh EH8 9YL, United Kingdom
  • MR Author ID: 1393409
  • Email: jeff.hicks@ed.ac.uk
  • Received by editor(s): December 7, 2023
  • Received by editor(s) in revised form: November 8, 2024
  • Published electronically: December 11, 2024
  • Additional Notes: The second author was supported by EPSRC Grant EP/V049097/1 (Lagrangians from Algebra and Combinatorics).
  • Communicated by: Jerzy Weyman
  • © Copyright 2024 by the authors under Creative Commons Attribution 3.0 License (CC BY 3.0)
  • Journal: Proc. Amer. Math. Soc. Ser. B 11 (2024), 653-663
  • MSC (2020): Primary 14F08, 18G80
  • DOI: https://doi.org/10.1090/bproc/252