Integration in valued fields
We develop a theory of integration over valued fields of residue characteristic zero. In particular we obtain new and base-field independent foundations for integration over local fields of large residue characteristic, extending results of Denef,Loeser, Cluckers. The method depends on an analysis o...
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| Format: | Journal article |
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Springer
2006
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| _version_ | 1797064447985975296 |
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| author | Hrushovski, E Kazhdan, D |
| author2 | Ginzburg, V |
| author_facet | Ginzburg, V Hrushovski, E Kazhdan, D |
| author_sort | Hrushovski, E |
| collection | OXFORD |
| description | We develop a theory of integration over valued fields of residue characteristic zero. In particular we obtain new and base-field independent foundations for integration over local fields of large residue characteristic, extending results of Denef,Loeser, Cluckers. The method depends on an analysis of definable sets up to definable bijections. We obtain a precise description of the Grothendieck semigroup of such sets in terms of related groups over the residue field and value group. This yields new invariants of all definable bijections, as well as invariants of measure preserving bijections. |
| first_indexed | 2024-03-06T21:14:26Z |
| format | Journal article |
| id | oxford-uuid:3f48e02b-c313-4ef3-a3f2-e983a5f0149a |
| institution | University of Oxford |
| last_indexed | 2024-03-06T21:14:26Z |
| publishDate | 2006 |
| publisher | Springer |
| record_format | dspace |
| spelling | oxford-uuid:3f48e02b-c313-4ef3-a3f2-e983a5f0149a2022-03-26T14:31:07ZIntegration in valued fieldsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:3f48e02b-c313-4ef3-a3f2-e983a5f0149aSymplectic Elements at OxfordSpringer2006Hrushovski, EKazhdan, DGinzburg, VWe develop a theory of integration over valued fields of residue characteristic zero. In particular we obtain new and base-field independent foundations for integration over local fields of large residue characteristic, extending results of Denef,Loeser, Cluckers. The method depends on an analysis of definable sets up to definable bijections. We obtain a precise description of the Grothendieck semigroup of such sets in terms of related groups over the residue field and value group. This yields new invariants of all definable bijections, as well as invariants of measure preserving bijections. |
| spellingShingle | Hrushovski, E Kazhdan, D Integration in valued fields |
| title | Integration in valued fields |
| title_full | Integration in valued fields |
| title_fullStr | Integration in valued fields |
| title_full_unstemmed | Integration in valued fields |
| title_short | Integration in valued fields |
| title_sort | integration in valued fields |
| work_keys_str_mv | AT hrushovskie integrationinvaluedfields AT kazhdand integrationinvaluedfields |