BEGIN:VCALENDAR
VERSION:2.0
PRODID:researchseminars.org
CALSCALE:GREGORIAN
X-WR-CALNAME:researchseminars.org
BEGIN:VEVENT
SUMMARY:Will Sawin (Columbia)
DTSTART:20230120T200000Z
DTEND:20230120T210000Z
DTSTAMP:20260407T214859Z
UID:agstanford/102
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/agstanford/1
 02/">Quantitative $\\ell$-adic sheaf theory</a>\nby Will Sawin (Columbia) 
 as part of Stanford algebraic geometry seminar\n\nLecture held in Room 383
 -N.\n\nAbstract\nSheaf cohomology is a powerful tool both in algebraic \ng
 eometry and its applications to other fields. Often\, one wants to \nprove
  bounds for the dimension of sheaf cohomology groups. Katz gave \nbounds f
 or the dimension of the étale cohomology groups of a variety \nin terms o
 f its defining equations (degree\, number of equations\, \nnumber of varia
 bles). But the utility of sheaf cohomology arises less \nfrom the ability 
 to compute the cohomology of varieties and more from \nthe toolbox of func
 tors that let us construct new sheaves from old\, \nwhich we often apply i
 n quite complicated sequences. In joint work \nwith Arthur Forey\, Javier 
 Fresán\, and Emmanuel Kowalski\, we prove \nbounds for the dimensions of 
 étale cohomology groups which are \ncompatible with the six functors form
 alism (and other functors \nbesides) in the sense that we define the “co
 mplexity” of a sheaf and \ncontrol how much the complexity can grow when
  we apply one of these \noperations.\n
LOCATION:https://researchseminars.org/talk/agstanford/102/
END:VEVENT
END:VCALENDAR