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

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.

Location: 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.

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.