A historical overview of pro cdh descent in algebraic $K$-theory and its relation to rigid analytic varieties

Matthew Morrow

A historical overview of pro cdh descent in algebraic $K$-theory and its relation to rigid analytic varieties

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arxiv 1612.00418 v1 pith:DZWY7ODK submitted 2016-12-01 math.KT math.AG

Matthew Morrow This is my paper · ORCID

classification math.KTmath.AG

keywords descentalgebraicanalyticnoterigidtheoryvarietiesapplications

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abstract

This note was prepared after the workshop on cdh descent and algebraic $K$-theory in Hara-mura, Japan (1 - 5 Sept. 2016), to complement the author's talk on the history and applications of pro cdh descent. In the final section pro cdh descent is used to define $K$-groups of rigid analytic varieties. This note was revised and released in light of Kerz, Strunk, and Tamme establishing pro cdh descent in general (arXiv:1611.08466).

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Dualizable Additive Categories
math.AT 2026-08 conditional novelty 8.0 of 10

Dualizable additive categories are characterized intrinsically and via almost modules, and a universal finitary localizing invariant (prestable motives) is constructed whose unit corepresents algebraic K-theory.

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