| Title:
|
The standard realizations for the $K$-theory of varieties (English) |
| Author:
|
Braunling, Oliver |
| Author:
|
Groechenig, Michael |
| Author:
|
Nanavaty, Anubhav |
| Language:
|
English |
| Journal:
|
Higher Structures |
| ISSN:
|
2209-0606 |
| Volume:
|
10 |
| Issue:
|
1 |
| Year:
|
2026 |
| Pages:
|
1-21 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The Grothendieck ring of varieties admits well-known realization maps to, say, mixed Hodge structures or compactly supported $\ell$-adic cohomology. These are often called motivic measures. Zakharevich and Campbell have developed a spectral refinement of the Grothendieck ring of varieties. We develop a realization map from their refinement to the $K$-theory of mixed motives. Composing the latter with the standard realizations of motives, this yields spectral refinements of all the usual motivic measures. (English) |
| Keyword:
|
Grothendieck ring of varieties |
| Keyword:
|
assembler |
| Keyword:
|
motivic measure |
| MSC:
|
14E99 |
| MSC:
|
19E99 |
| DOI:
|
10.21136/HS.2026.01 |
| . |
| Date available:
|
2026-09-17T12:40:33Z |
| Last updated:
|
2026-09-17 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/153751 |
| . |
| Reference:
|
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