The Beilinson fiber square
[Moved Online] (∞, n)-categories, factorization homology, and algebraic K-theory March 23, 2020 - March 27, 2020
Location: MSRI: Online/Virtual
deformation of algebraic cycles
19D55 - $K$-theory and homology; cyclic homology and cohomology [See also 18G60]
19E15 - Algebraic cycles and motivic cohomology [See also 14C25, 14C35, 14F42]
If R is an associative ring satisfying some mild technical conditions, Beilinson constructs a fiber sequence of spectra identifying the fiber of the map \lim_n K(R/p^n)\rightarrow K(R/p) with a suspension of the ordinary cyclic homology of R, all up to p-completion followed by inverting p. Joint work with Akhil Mathew, Matthew Morrow, and Thomas Nikolaus provides a new proof of this fact using recent advances in the theory of cyclotomic spectra due to Nikolaus and Scholze. I will explain the motivation for this fiber sequence, which has to do with the infinitesimal part of the p-adic variational Hodge conjecture, and then I will give a construction of the fiber sequence and of a more general fiber square.
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