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SUMMARY:Ben Briggs (University of Utah)
DTSTART:20200915T133000Z
DTEND:20200915T143000Z
DTSTAMP:20260423T035026Z
UID:VCAS/21
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/VCAS/21/">On
  a conjecture of Vasconcelos - Part 1</a>\nby Ben Briggs (University of Ut
 ah) as part of IIT Bombay Virtual Commutative Algebra Seminar\n\n\nAbstrac
 t\nThese two talks are about the following theorem: If I is an ideal of fi
 nite projective dimension in a ring $R\,$ and the conormal module $I/I^2$ 
 has finite projective dimension over R/I\, then I is locally generated by 
 a regular sequence. This was conjectured by Vasconcelos\, after he and (se
 parately) Ferrand established the case that the conormal module is project
 ive.\n\nThe key tool is the homotopy Lie algebra\, an object sitting at th
 e centre of a bridge between commutative algebra and rational homotopy the
 ory. In the first part I will explain what the homotopy Lie algebra is\, a
 nd how it can be constructed by differential graded algebra techniques\, f
 ollowing the work of Avramov. In the second part I will bring all of the i
 ngredients together and\, hopefully\, present the proof of Vasconcelos' co
 njecture.\n
LOCATION:https://researchseminars.org/talk/VCAS/21/
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