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SUMMARY:Rothschild Lecture:  Higher algebra and arithmetic - Monday 8th Oc
 tober 2018 - Lars Hesselholt (Nagoya University\; University of Copenhagen
 )
DTSTART:20181008T150000Z
DTEND:20181008T160000Z
UID:TALK111136@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:This talk concerns a twenty-thousand-year old mistake: The nat
 ural numbers record only the result of counting and not the process of cou
 nting. As algebra is rooted in the natural numbers\, the higher of Joyal a
 nd Lurie is rooted in a more basic notion of number which also records the
  process of counting. Long advocated by Waldhausen\, the arithmetic of the
 se more basic numbers should eliminate denominators. Notable manifestation
 s of this vision include the B&ouml\;kstedt-Hsiang-Madsen topological cycl
 ic homology\, which receives a denominator-free Chern character\, and the 
 related Bhatt-Morrow-Scholze integral p-adic Hodge theory\, which makes it
  possible to exploit torsion cohomology classes in arithmetic geometry. Mo
 reover\, for schemes smooth and proper over a finite field\, the analogue 
 of de Rham cohomology in this setting naturally gives rise to a cohomologi
 cal interpretation of the Hasse-Weil zeta function by regularized determin
 ants\, as envisioned by Deninger.
LOCATION:Seminar Room 1\, Newton Institute
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