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SUMMARY:Thom-Sebastiani theorem in the motivic world
DTSTART:20250918T131500
DTEND:20250918T150000
DTSTAMP:20260412T213206Z
UID:6a0c3610239cd5cf550f2b8a049db03cb75a208cd90d93701c72d18c
CATEGORIES:Conferences - Seminars
DESCRIPTION:Pierre Descombes\nSebastiani and Thom proved\, in the complex 
 analytic setting\, that the vanishing cycle of f+g is the product of the v
 anishing cycles of f and g. In the motivic world\, Deligne has observed th
 at such a formula cannot hold\, unless one considers instead the convoluti
 on product with respect to the monodromy. This formula was then obtained f
 or étale sheaves by Illusie\, and for mixed Hodge modules by Saito. We wi
 ll present here a proof working for Morel-Voevodsky motivic stable homotop
 y theory (SH)\, using deep results of Ayoub. Passing to the Grothendieck g
 roup\, one obtains the Thom-Sebastiani theorem of Denef-Loeser-Looijenga.\
 nWe will then explain how\, using this result\, vanishing cycles of quadra
 tic forms give square roots of Thom twists\, generalizing the results of D
 eligne for étale sheaves. We will then sketch how these results could be 
 used to upgrade cohomological DT theory at the level of SH\, up to some im
 portant orientation issues.
LOCATION:CM 1 517 https://plan.epfl.ch/?room==CM%201%20517
STATUS:CONFIRMED
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