Construction of an Overconvergent Relative de Rham-Witt Complex - Mathematics - EPSRC DTP funded PhD Studentship Ref: 2883

About the award

This project is one of a number funded by the Engineering and Physical Sciences Research Council (EPSRC) Doctoral Training Partnership to commence in September 2018. This project is in direct competition with others for funding; the projects which receive the best applicants will be awarded the funding.

The studentships will provide funding for a stipend which is currently £14,553 per annum for 2017-2018. It will provide research costs and UK/EU tuition fees at Research Council UK rates for 42 months (3.5 years) for full-time students, pro rata for part-time students.

Please note that of the total number of projects within the competition, up to 15 studentships will be filled.

Prof. Andreas Langer
Professor Nigel Byott

Streatham Campus, Exeter

Project Description

A PhD-studentship is available to study a central problem in relative p-adic Hodge-theory.

For a scheme X which is smooth over a characteristic p scheme S a relative de Rham-Witt complex has been constructed that computes relative crystalline cohomology. If X is not proper then a better cohomology theory is relative rigid cohomology which was constructed by Shiho.

In the project an overconvergent version of the relative de Rham-Witt complex needs to be constructed that extends the complex of Davis/Langer/Zink for the case that S is a perfect field ( a project funded by EPSRC) to a relative setting and computes relative rigid cohomology. The next step is then to describe the higher direct images of the rig-functor from overconvergent isocrystals on X to overconvergent isocrystals on S.

Entry Requirements
You should have or expect to achieve a First Class degree, or equivalent, in Mathematics. Experience and basic knowledge in algebraic geometry is desirable; a strong interest to study new techniques in arithmetic geometry is necessary.

The majority of the studentships are available for applicants who are ordinarily resident in the UK and are classed as UK/EU for tuition fee purposes.  If you have not resided in the UK for at least 3 years prior to the start of the studentship, you are not eligible for a maintenance allowance so you would need an alternative source of funding for living costs. To be eligible for fees-only funding you must be ordinarily resident in a member state of the EU.  For information on EPSRC residency criteria click here.

Applicants who are classed as International for tuition fee purposes are NOT eligible for funding. International students interested in studying at the University of Exeter should search our funding database for alternative options.


Application deadline:10th January 2018
Value:3.5 year studentship: UK/EU tuition fees and an annual maintenance allowance at current Research Council rate. Current rate of £14,553 per year.
Duration of award:per year
Contact: Doctoral

How to apply

You will be required to upload the following documents:
•       CV
•       Letter of application outlining your academic interests, prior research experience and reasons for wishing to
        undertake the project.
•       Transcript(s) giving full details of subjects studied and grades/marks obtained.  This should be an interim
        transcript if you are still studying.
•       If you are not a national of a majority English-speaking country you will need to submit evidence of your current
        proficiency in English.  For further details of the University’s English language requirements please see

The closing date for applications is midnight (GMT) on Wednesday 10 January 2018.  Interviews will be held at the University of Exeter in late February 2018.

If you have any general enquiries about the application process please email:
Project-specific queries should be directed to the supervisor.

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• the selection panel and/or management board or equivalent of the relevant programme, which is likely to include staff from one or more other HEIs;
• administrative staff at one or more other HEIs participating in the relevant programme.

Such disclosures will always be kept to the minimum amount of personal data required for the specific purpose. Your sensitive personal data (relating to disability and race/ethnicity) will not be disclosed without your explicit consent.