---
- CiteKey: "CZ21"
- Type: journalArticle
- Title: "Hilbert's third problem and a conjecture of Goncharov," 
- Author: "Campbell, Jonathan; Zakharevich, Inna;"  
- Year: 2019 
- DOI: 10.48550/arXiv.1910.07112
- Collections: "Syllabus; Talbot 2022,"
---

# Hilbert's third problem and a conjecture of Goncharov

## Meta

- **URL**: <https://arxiv.org/abs/1910.07112v8>
- **URI**: <http://zotero.org/users/1049732/items/NKFP6ZRG>
- **Local File**: [Full Text PDF](file:///home/zack/Zotero/storage/AB5ML49Y/Campbell%20and%20Zakharevich%20-%202019%20-%20Hilbert's%20third%20problem%20and%20a%20conjecture%20of%20Goncha.pdf)
- **Open in Zotero**: [Zotero](zotero://select/library/items/NKFP6ZRG)

## Abstract

In this paper we reduce the generalized Hilbert's third problem about Dehn invariants and scissors congruence classes to the injectivity of certain Chern--Simons invariants. We also establish a version of a conjecture of Goncharov relating scissors congruence groups of polytopes and the algebraic $K$-theory of $\mathbf{C}$.

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