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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Rothschild Lecture: Higher algebra and arithmetic
- Monday 8th October 2018 - Lars Hesselholt (Nago
ya University\; University of Copenhagen)
DTSTART;TZID=Europe/London:20181008T160000
DTEND;TZID=Europe/London:20181008T170000
UID:TALK111136AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/111136
DESCRIPTION:This talk concerns a twenty-thousand-year old mist
ake: The natural numbers record only the result of
counting and not the process of counting. As alge
bra is rooted in the natural numbers\, the higher
of Joyal and Lurie is rooted in a more basic notio
n of number which also records the process of coun
ting. Long advocated by Waldhausen\, the arithmeti
c of these more basic numbers should eliminate den
ominators. Notable manifestations of this vision i
nclude the Bö\;kstedt-Hsiang-Madsen topologica
l cyclic homology\, which receives a denominator-f
ree Chern character\, and the related Bhatt-Morrow
-Scholze integral p-adic Hodge theory\, which make
s it possible to exploit torsion cohomology classe
s in arithmetic geometry. Moreover\, for schemes s
mooth and proper over a finite field\, the analogu
e of de Rham cohomology in this setting naturally
gives rise to a cohomological interpretation of th
e Hasse-Weil zeta function by regularized determin
ants\, as envisioned by Deninger.
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:INI IT
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