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SUMMARY:De Rham cohomology: from smooth algebraic varieties to dagger geom
 etry - Tom Adams\, University of Cambridge
DTSTART:20240209T160000Z
DTEND:20240209T170000Z
UID:TALK209290@talks.cam.ac.uk
CONTACT:Alexis Marchand
DESCRIPTION:In this talk\, I will begin by reviewing the definition of alg
 ebraic de Rham cohomology\, for a smooth complex algebraic variety X\, and
  recalling a well-known result of Grothendieck which relates this cohomolo
 gy to the singular cohomology of the analytification of X. One of the shor
 tcomings of Tate’s model of non-archimedean geometry is that the algebra
 ic approach to de Rham cohomology does not generalise to give a satisfacto
 ry theory in this setting. In the remainder of my talk\, I will explain wh
 y this is the case and\, if there is time\, illustrate how Grosse-Klonne f
 ixed this problem through the introduction of dagger spaces.
LOCATION:MR4
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