# The Beilinson fiber square

## [Moved Online] (∞, n)-categories, factorization homology, and algebraic K-theory March 23, 2020 - March 27, 2020

**Speaker(s):**Benjamin Antieau (Northwestern University)

**Location:**SLMath: Online/Virtual

**Tags/Keywords**

p-adic K-theory

cyclic homology

deformation of algebraic cycles

motivic cohomology

**Primary Mathematics Subject Classification**

14G40 - Arithmetic varieties and schemes; Arakelov theory; heights [See also 11G50, 37P30]

18M65 - Non-symmetric operads, multicategories, generalized multicategories

18M85 - Polycategories/dioperads, properads, PROPs, cyclic operads, modular operads

**Secondary Mathematics Subject Classification**No Secondary AMS MSC

#### 3-Antieau

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.

#### 3-Antieau

H.264 Video | 918_28231_8258_3-Antieau.mp4 |

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