---
title: "The standard realizations for the K-theory of varieties"
status: read-1x
tags: projects/talbot-talk 
---

# The standard realizations for the K-theory of varieties

## Meta

- **CiteKey**: "BGN21"
- **Type**: report
- **Title**: "The standard realizations for the K-theory of varieties," 
- **Author**: "Braunling, Oliver; Groechenig, Michael; Nanavaty, Anubhav;"  
- **Publisher**: "arXiv,"
- **Year**: 2021 
- **Collections**: "Syllabus; Talbot 2022,"
- **Keywords**: "Mathematics - Algebraic Geometry"; "Mathematics - Algebraic Topology"
- **URL**: <http://arxiv.org/abs/2107.01168>
- **Local File**: [arXiv.org Snapshot](file:///home/zack/Zotero/storage/GI743U64/2107.html); [Braunling et al. - 2021 - The standard realizations for the K-theory of vari.pdf](file:///home/zack/Downloads/Zotero_Source/arXiv/2021/Braunling%20et%20al.%20-%202021%20-%20The%20standard%20realizations%20for%20the%20K-theory%20of%20vari.pdf)
- **Open in Zotero**: [Zotero](zotero://select/library/items/XL898QAN)

## Abstract

The Grothendieck ring of varieties has well-known realization maps to, say, mixed Hodge structures or compactly supported $\ell$-adic cohomology. Zakharevich and\ Campbell have developed {a spectral refinement} of the Grothendieck ring of varieties. We develop a realization map to Voevodsky mixed motives, and this lifts the standard realizations of motives to this setting, at least over perfect fields which have resolution of singularities.

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## Extracted Annotations


Annotations(6/8/2022, 8:26:54 PM)

![[BGN21_67YSU6XV.png]] [(Braunling et al., 2021, p. 1)](zotero://open-pdf/library/items/R3DGVTJS?page=1&annotation=4KG589Y9)

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