| EPSRC Reference: |
EP/T005351/1 |
| Title: |
Integral p_adic Hodge-theory and applications to p-adic deformation theory |
| Principal Investigator: |
Langer, Professor A |
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| Department: |
Mathematics |
| Organisation: |
University of Exeter |
| Scheme: |
Standard Research |
| Starts: |
01 January 2020 |
Ends: |
31 December 2022 |
Value (£): |
381,961
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| No relevance to Underpinning Sectors |
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Summary on Grant Application Form |
We associate linear data to geometric objects like curves, surfaces or threefolds defined as zero-sets of algebraic equations over the integers or over a number domain that is annihilated by a power of a prime number. One can ask how much information about the original object can be captured in this way. The linear data are given by various cohomology theories which is a standard technique in many areas in Pure Mathematics including topology, complex and arithmetic geometry. This problem leads to what is called p-adic deformation theory; the project addresses the question in the case of crystalline cohomology or equivalently de Rham-Witt cohomology classes associated to algebraic cycles and how they deform p-adically. A related problem of particular interest is to identify an integral structure defined over the (p-adic) integers inside these linear data which leads to finer invariants of the geometric objects and encode more information. This method is very common in arithmetic geometry.
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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 |