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SUMMARY:Benjamin Briggs (University of Utah)
DTSTART:20200806T203000Z
DTEND:20200806T220000Z
DTSTAMP:20260423T021436Z
UID:FOTR/14
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/FOTR/14/">Th
 e homotopy Lie algebra and the conormal module</a>\nby Benjamin Briggs (Un
 iversity of Utah) as part of Fellowship of the Ring\n\n\nAbstract\nI will 
 do my best to explain what goes in to proving the following theorem: if $I
 $ is an ideal of finite projective dimension in a local ring $R$\, and the
  conormal module $I/I^2$ has finite projective dimension over $R/I$\, then
  $I$ is generated by a regular sequence. This was conjectured by Vasconcel
 os\, after he and (separately) Ferrand established the case that the conor
 mal module is free.\n\nThe key tool is the homotopy Lie algebra. This is a
  graded Lie algebra naturally associated with any local homomorphism. It s
 its at the centre of a longstanding friendship between commutative algebra
  and rational homotopy theory\, through which ideas and results have been 
 passed back and forth for decades.\n\nI'll go through the construction of 
 the homotopy Lie algebra and how it's been used in commutative algebra in 
 the past\, before explaining how its structure detects when the conormal m
 odule has finite projective dimension. I'll also talk about ongoing work w
 ith Srikanth Iyengar comparing the cotangent complex with the homotopy Lie
  algebra.\n
LOCATION:https://researchseminars.org/talk/FOTR/14/
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