@article{c24775c91e004cfca3cc1f175acd023f,
title = "A category of kernels for equivariant factorizations, II: Further implications",
abstract = "We leverage the results of the prequel [8], in combination with a theorem of D. Orlov to create a categorical covering picture for factorizations. As applications, we provide a conjectural geometric framework to further understand M. Kontsevich's Homological Mirror Symmetry conjecture and obtain new cases of a conjecture of Orlov concerning the Rouquier dimension of the bounded derived category of coherent sheaves on a smooth variety.",
keywords = "Derived categories, Homological Mirror Symmetry, Matrix factorizations, Rouquier dimension",
author = "Matthew Ballard and David Favero and Ludmil Katzarkov",
note = "Funding Information: The authors are greatly appreciative of the valuable insight gained from conversations and correspondence with Mohammed Abouzaid, Denis Auroux, Andrei C{\u a}ld{\u a}raru, Dragos Deliu, Colin Diemer, Tobias Dyckerhoff, Manfred Herbst, M. Umut Isik, Gabriel Kerr, Maxim Kontsevich, Jacob Lewis, Dmitri Orlov, Pranav Pandit, Tony Pantev, Anatoly Preygel, Victor Przyjalkowski, Ed Segal, Paul Seidel, and Paolo Stellari and would like to thank them for their time and patience. Furthermore, the authors are deeply grateful to Alexander Polishchuk and Arkady Vaintrob for providing us with a preliminary version of their work [49] and for allowing us time to prepare the original version of this paper in order to synchronize arXiv posting of the articles due to the overlap. The second named author would also like to thank the Korean Institute for Advanced Study for its hospitality during final preparation of this document. The first named author was funded by NSF DMS 0636606 RTG , NSF DMS 0838210 RTG , and NSF DMS 0854977 FRG . The second and third named authors were funded by NSF DMS 0854977 FRG , NSF DMS 0600800 , NSF DMS 0652633 FRG , NSF DMS 0854977 , NSF DMS 0901330 , FWF P24572 N25 , by FWF P20778 and by an ERC Grant. Publisher Copyright: {\textcopyright} 2014 Elsevier Masson SAS.",
year = "2014",
month = oct,
day = "1",
doi = "10.1016/j.matpur.2014.02.004",
language = "English (US)",
volume = "102",
pages = "702--757",
journal = "Journal des Mathematiques Pures et Appliquees",
issn = "0021-7824",
publisher = "Elsevier Masson SAS",
number = "4",
}