Measures on higher dimensional local fields and algebraic groups on them
This thesis is about defining finitely additive measures on sets. The prototype for what we’re doing is defining a R((X))-valued measure on a 2dimensional local field (such as Qp{{t}}). The thesis consists of three main parts. The first part consists of defining finitely additive measures and integration i...
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| Format: | Thesis (University of Nottingham only) |
| Language: | English |
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2020
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| Online Access: | https://eprints.nottingham.ac.uk/63889/ |
| _version_ | 1848800070084853760 |
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| author | van Urk, Wester |
| author_facet | van Urk, Wester |
| author_sort | van Urk, Wester |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | This thesis is about defining finitely additive measures on sets. The prototype for what we’re doing is defining a R((X))-valued measure on a 2dimensional local field (such as Qp{{t}}). The thesis consists of three main parts. The first part consists of defining finitely additive measures and integration in relatively high degree of generality so that we can not only integrate over 2-dimensional local fields but also higher dimensional local fields, C((t)) and over algebraic groups. The second part consists of applying this theory to obtain a sequence of more refined measures µn on a 2-dimensional local field which allow us to define the Fourier transform intrinsically. The third and final part consists of applying the theory to coset measures on GL(2) and SL(2), including rigorously defining a local Hecke operator on GL(2,C((t))). |
| first_indexed | 2025-11-14T20:45:42Z |
| format | Thesis (University of Nottingham only) |
| id | nottingham-63889 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-14T20:45:42Z |
| publishDate | 2020 |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-638892025-02-28T12:24:23Z https://eprints.nottingham.ac.uk/63889/ Measures on higher dimensional local fields and algebraic groups on them van Urk, Wester This thesis is about defining finitely additive measures on sets. The prototype for what we’re doing is defining a R((X))-valued measure on a 2dimensional local field (such as Qp{{t}}). The thesis consists of three main parts. The first part consists of defining finitely additive measures and integration in relatively high degree of generality so that we can not only integrate over 2-dimensional local fields but also higher dimensional local fields, C((t)) and over algebraic groups. The second part consists of applying this theory to obtain a sequence of more refined measures µn on a 2-dimensional local field which allow us to define the Fourier transform intrinsically. The third and final part consists of applying the theory to coset measures on GL(2) and SL(2), including rigorously defining a local Hecke operator on GL(2,C((t))). 2020-12-11 Thesis (University of Nottingham only) NonPeerReviewed application/pdf en arr https://eprints.nottingham.ac.uk/63889/1/thesis.pdf van Urk, Wester (2020) Measures on higher dimensional local fields and algebraic groups on them. MPhil thesis, University of Nottingham. Set theory Finitely additive measures Dimensional local fields Fourier transformations. |
| spellingShingle | Set theory Finitely additive measures Dimensional local fields Fourier transformations. van Urk, Wester Measures on higher dimensional local fields and algebraic groups on them |
| title | Measures on higher dimensional local fields and algebraic groups on them |
| title_full | Measures on higher dimensional local fields and algebraic groups on them |
| title_fullStr | Measures on higher dimensional local fields and algebraic groups on them |
| title_full_unstemmed | Measures on higher dimensional local fields and algebraic groups on them |
| title_short | Measures on higher dimensional local fields and algebraic groups on them |
| title_sort | measures on higher dimensional local fields and algebraic groups on them |
| topic | Set theory Finitely additive measures Dimensional local fields Fourier transformations. |
| url | https://eprints.nottingham.ac.uk/63889/ |