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SUMMARY:Zijian Yao (Harvard)
DTSTART:20200527T230000Z
DTEND:20200527T235000Z
DTSTAMP:20260423T022829Z
UID:UCLA_NTS/4
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/UCLA_NTS/4/"
 >Crystalline comparison of $\\mathrm{A}_\\mathrm{inf}$-cohomology</a>\nby 
 Zijian Yao (Harvard) as part of UCLA Number Theory Seminar\n\n\nAbstract\n
 A major goal of $p$-adic Hodge theory is to relate arithmetic structures c
 oming from various cohomology theories of $p$-adic varieties. Such compari
 sons are usually achieved by constructing intermediate cohomology theories
 . A somewhat recent successful theory\, namely the $\\mathrm{A}_\\mathrm{i
 nf}$-cohomology\, has been invented by Bhatt--Morrow--Scholze\, originally
  via perfectoid spaces. In this talk\, I will describe a simpler approach 
 to prove the comparison between $\\mathrm{A}_\\mathrm{inf}$-cohomology and
  the crystalline cohomology over Fontaine's period ring $\\mathrm{A}_\\mat
 hrm{cris}$\, using flat descent of cotangent complexes. This approach also
  allows us to prove compatibilities of certain $p$-adic filtrations. Time 
 permitting\, I will discuss some work in progress (partially joint with Ha
 nsheng Diao) in the semistable/logarithmic case.\n
LOCATION:https://researchseminars.org/talk/UCLA_NTS/4/
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