Tallennettuna:
| Päätekijät: | , |
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| Aineistotyyppi: | Recurso digital |
| Kieli: | |
| Julkaistu: |
Zenodo
2026
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| Aiheet: | |
| Linkit: | https://doi.org/10.5281/zenodo.18763366 |
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Sisällysluettelo:
- We construct a canonical motivic measure on the category of smooth rigid analytic varieties over a discretely valued field K, taking values in a completion of the Grothendieck ring of varieties extended by rational powers of the Lefschetz motive. By bridging the model-theoretic integration of Hrushovski-Kazhdan with the geometric formalism of Berkovich spaces, we establish a comparison isomorphism between the motivic volume of a bounded semi-algebraic set and the weight-graded pieces of its compactly supported étale cohomology. Furthermore, we analyze the behavior of the motivic zeta function under the tropicalization map, proving a non-archimedean analogue of the Monodromy Conjecture for the analytic Milnor fiber. Our results provide a cohomological interpretation of the motivic volume in terms of the weight filtration on the vanishing cycles sheaf, generalizing the work of Denef and Loeser to the analytic setting.