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SUMMARY:Derived analytic geometry through localized contexts [MPIM]
DTSTART:20260707T130500Z
DTEND:20260707T150000Z
DTSTAMP:20260623T225400Z
UID:indico-event-1427@math-events.uni-bonn.de
DESCRIPTION:Speakers: Jeroen Hekking (Stockholms University)\n\nObersemina
 r Arithmetic Geometry and Representation Theory\nClassically\, HKR identif
 ies Hochschild homology with differential    forms in the smooth settin
 g. Ben-Zvi--Nadler interpret this    comparison through derived loop sp
 aces in characteristic zero.    Outside characteristic zero\, Raksit's 
 nonconnective affine formalism    produces an HKR filtration on Hochsch
 ild homology whose associated    graded recovers the derived de Rham si
 de of the theory.\n    In analytic geometry\, the exactness needed for 
 derived constructions    often clashes with completeness. One response 
 is to develop    homological algebra in Quillen-exact categories. The c
 ondensed    approach replaces topology by condensed structure\, yieldin
 g an    abelian category\, and axiomatizes completeness through analyti
 c    rings. This leads to the question: can one formulate HKR-type  
   results uniformly across derived analytic geometries?\n    I will re
 port on work in progress with Oren Ben-Bassat and Jack    Kelly on a co
 mmon framework for asking this question\, at least in    the affine set
 ting. The framework is based on localized contexts\, a    generalizatio
 n of derived algebraic contexts. I will introduce    analytic rings ove
 r localized contexts and discuss examples coming    from non-Archimedea
 n analytic geometry\, light condensed mathematics\,    and adic complet
 ion. If time permits\, I will indicate how cotangent    complexes and n
 onconnective analytic rings enter the intended route    toward unified 
 and global HKR-type statements.\n \n\nhttps://math-events.uni-bonn.de/eve
 nt/1427/
LOCATION:MPIM\, Vivatsgasse\,  7 - Lecture Hall (Max Planck Institute for 
 Mathematics)
URL:https://math-events.uni-bonn.de/event/1427/
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