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Details of Grant 

EPSRC Reference: EP/T005351/1
Title: Integral p_adic Hodge-theory and applications to p-adic deformation theory
Principal Investigator: Langer, Professor A
Other Investigators:
Researcher Co-Investigators:
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:
Algebra & Geometry
EPSRC Industrial Sector Classifications:
No relevance to Underpinning Sectors
Related Grants:
Panel History:
Panel DatePanel NameOutcome
21 May 2019 EPSRC Mathematical Sciences Prioritisation Panel May 2019 Announced
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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Organisation Website: http://www.ex.ac.uk