EPSRC Reference: 
EP/T005351/1 
Title: 
Integral p_adic Hodgetheory and applications to padic deformation theory 
Principal Investigator: 
Langer, Professor A 
Other Investigators: 

Researcher CoInvestigators: 

Project Partners: 

Department: 
Mathematical Sciences 
Organisation: 
University of Exeter 
Scheme: 
Standard Research 
Starts: 
01 January 2020 
Ends: 
31 December 2022 
Value (£): 
381,961

EPSRC Research Topic Classifications: 

EPSRC Industrial Sector Classifications: 
No relevance to Underpinning Sectors 


Related Grants: 

Panel History: 

Summary on Grant Application Form 
We associate linear data to geometric objects like curves, surfaces or threefolds defined as zerosets 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 padic deformation theory; the project addresses the question in the case of crystalline cohomology or equivalently de RhamWitt cohomology classes associated to algebraic cycles and how they deform padically. A related problem of particular interest is to identify an integral structure defined over the (padic) 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.

Key Findings 
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Potential use in nonacademic contexts 
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Impacts 
Description 
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Summary 

Date Materialised 


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Project URL: 

Further Information: 

Organisation Website: 
http://www.ex.ac.uk 