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SUMMARY:Strictly commutative algebras in positive characteristic
DTSTART:20240917T120000Z
DTEND:20240917T130000Z
DTSTAMP:20240915T074100Z
UID:indico-event-12359@indico.math.cnrs.fr
DESCRIPTION:Speakers: Oisin Flynn-Connolly (Paris 13)\n\nIn this talk\, wh
ich consists of two parts\, we study the relationship between strictly com
mutative dg-algebras\, topological spaces and $E_\\infty$-algebras in posi
tive and mixed characteristics.\n \nIn the first part\, we work over $F_
p$. We define a general theory of higher cohomology operations called cotr
iple products and compute the secondary cohomology operations for a strict
ly commutative dg-algebra. We study the induced obstruction theory\, produ
cing several counterexamples. We conclude by showing a $E_\\infty$ -al
gebra over $F_p$ admits a commutative model if and only if its higher
Steenrod operations vanish coherently. \n \nIn the second part\, we gene
ralise the de Rham forms to the p-adic numbers\, thus providing a best str
ictly commutative approximation to the singular cochains complex in this c
ontext. We study the question of its formality and discuss Massey products
. We remark on some connections to crystalline cohomology for schemes. \n
\nhttps://indico.math.cnrs.fr/event/12359/
LOCATION:IMT 1R2 207 (Salle Pellos)
URL:https://indico.math.cnrs.fr/event/12359/
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