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SUMMARY:Shachar Carmeli (WIS)
DTSTART:20200603T133000Z
DTEND:20200603T143000Z
DTSTAMP:20260423T005834Z
UID:AlgWies/2
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/AlgWies/2/">
 A relative de Rham theorem for Nash Submersions</a>\nby Shachar Carmeli (W
 IS) as part of Seminar on Representation Theory and Algebraic Geometry\n\n
 \nAbstract\nFor a Nash manifold X and a Nash vector bundle E on X\, one ca
 n form the topological vector space of Schwartz sections of E\, i.e. the s
 mooth sections which decay fast along with all derivatives.  It was shown 
 by Aizenbud and Gourevitch\, and independently by Luca Prelli\, that for a
  Nash manifold X\, th complex of Schwartz sections of the de Rham complex 
 of X has cohomologies isomorphic to the compactly supported cohomologies o
 f X. \n \nIn my talk I will present a work in progress\, joint with Avraha
 m Aizenbud\, to generalize this result to the relative case\, replacing th
 e Nash manifold M with a Nash submersion f:M-->N. Using infinity categoric
 al methods\, I will define the notion of a Schwartz section of a Nash bund
 le E over a complex of sheaves with constructible cohomologies\, generaliz
 ing the notion of Schwartz section on an open semialgebraic set. I will th
 en relate the Schwartz sections of the relative de Rham complex of a Nash 
 submersion f:M-->N with the Schwartz functions on N over the derived push-
 forward with proper support of the constant sheaf on M. Finally\, I will c
 oclude with some applications to the relation between the Schwartz section
 s of the relative de Rham complex and the topology of the fibers of f\n
LOCATION:https://researchseminars.org/talk/AlgWies/2/
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