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SUMMARY:Liran Shaul : The finitistic dimension conjecture via DG-rings
DTSTART;VALUE=DATE-TIME:20220919T120000Z
DTEND;VALUE=DATE-TIME:20220919T130000Z
DTSTAMP;VALUE=DATE-TIME:20221207T043800Z
UID:indico-event-8418@indico.math.cnrs.fr
DESCRIPTION:The finitistic dimension of a ring A is defined to be the supr
emum of projective dimensions among all A-modules of finite projective dim
ension. It is an open problem whether this quantity is finite for finite d
imensional algebras over a field and for artin algebras.In this talk\, I w
ill explain a new approach for studying the finiteness of the finitistic d
imension by embedding the ring A inside a nicely behaved differential grad
ed algebra\, and using relation between this DG-algebra and A to deduce re
sults about the finitistic dimension. As an application of these methods\,
I will explain how to generalize a recent sufficient condition of Rickard
\, for FPD(A)<∞ in terms of generation of D(A) from finite dimensional a
lgebras over a field to all left perfect rings which admit a dualizing com
plex.\n\nhttps://indico.math.cnrs.fr/event/8418/
URL:https://indico.math.cnrs.fr/event/8418/
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