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SUMMARY:Ishan Levy (MIT)
DTSTART:20210219T180000Z
DTEND:20210219T193000Z
DTSTAMP:20260422T220035Z
UID:STAGE/21
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/STAGE/21/">T
 he infinitesimal site and algebraic de Rham cohomology</a>\nby Ishan Levy 
 (MIT) as part of STAGE\n\n\nAbstract\nThe de Rham cohomology of the analyt
 ification of a smooth projective\nvariety over $\\mathbb{C}$ can be comput
 ed via an algebraic de Rham complex.\nUnfortunately\, the algebraic de Rha
 m complex is somewhat poorly behaved in\npositive characteristic.  To solv
 e this problem\, Grothendieck\nshowed first how to reinterpret de Rham coh
 omology in characteristic 0\nas cohomology on a site (the infinitesimal si
 te)\, and second\nhow to modify the infinitesimal site to obtain a site\nt
 hat works well also in characteristic p (the crystalline site).\n\nIn this
  talk\, we will explain algebraic de Rham cohomology\nand define the infin
 itesimal and stratifying sites. \nWe also will define the notion of a clas
 sical Weil cohomology theory\,\nwhich de Rham cohomology (char 0) and crys
 talline cohomology give examples of.\n
LOCATION:https://researchseminars.org/talk/STAGE/21/
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