| EPSRC Reference: |
GR/M91037/01 |
| Title: |
HOPF ORDERS, FORMAL GROUPS AND GALOIS MODULE STRUCTURE |
| Principal Investigator: |
Byott, Professor N |
| Other Investigators: |
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| Department: |
Mathematical Sciences |
| Organisation: |
University of Exeter |
| Scheme: |
Overseas Travel Grants Pre-FEC |
| Starts: |
01 September 1999 |
Ends: |
31 October 1999 |
Value (£): |
4,424
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| No relevance to Underpinning Sectors |
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Summary on Grant Application Form |
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Hopf orders and their principal homogeneous spaces can be constructed using formal groups, and this leads to interesting results in Galois module structure. We will use formal groups to investigate two problems relating to Hopf orders and Galois module structure. The first is to determine which Hopf orders have an integrally closed principal homogeneous space, and in particular to ascertain if monogeneity guarantees this. This is related to the question of whether every monogeneity Hopf order arises from an isogeny of 1-dimensional formal groups. We will also investigate connections with factor-equivalence, which is known to constrain the Hopf orders which can arise. The second problem is Waterhouse's conjecture that the principal homogeneous spaces realise all primitive classes in the Picard group. We seek to reinterpret previous work on this in terms of formal groups and their logarithms, in order to give a constructive proof of further cases of the conjecture.
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Key Findings |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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Potential use in non-academic contexts |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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Impacts |
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| Description |
This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk |
| Summary |
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| Date Materialised |
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Sectors submitted by the Researcher |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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| Project URL: |
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| Further Information: |
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| Organisation Website: |
http://www.ex.ac.uk |