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SUMMARY:CANCELLED $\\mathbb A^1$-connected components of ruled surfaces - 
 Anand Sawant (Tata Institute of Fundamental Research)
DTSTART:20200326T101000Z
DTEND:20200326T111000Z
UID:TALK141166@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:A conjecture of Morel asserts that the sheaf of $\\mathbb A^1$
 -connected components of a space is $\\mathbb A^1$-invariant.&nbsp\; We wi
 ll discuss how the sheaves of ``naive" as well as ``genuine" $\\mathbb A^1
 $-connected components of a smooth projective birationally ruled surface c
 an be determined using purely algebro-geometric methods.&nbsp\; We will di
 scuss a proof of Morel&#39\;s conjecture for a&nbsp\;smooth projective sur
 face birationally ruled over a curve of genus &gt\; 0 over an algebraicall
 y closed field of characteristic 0.&nbsp\; If time permits\, we will indic
 ate why the naive and genuine $\\mathbb A^1$-connected components of such 
 a birationally ruled surface do not coincide if the surface is not a minim
 al model and discuss some open questions and specultions regarding the sit
 uation in higher dimensions.&nbsp\; The talk is based on joint work with C
 hetan Balwe.
LOCATION:Seminar Room 1\, Newton Institute
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