EPSRC DTP PhD studentship: Overconvergent de Rham-Witt cohomology for semistable schemes

University of Exeter - College of Engineering, Mathematics and Physical Sciences

Main supervisor: Prof Andreas Langer (University of Exeter)

Co-supervisor: Prof Nigel Byott (University of Exeter)

In this project the PhD-student shall study a comparison theorem between rigid cohomology and overconvergent de Rham-Witt cohomology for smooth varieties which was funded by EPSRC and published jointly by Davis, Zink and the project supervisor and extend the result to semistable varieties resp log-schemes. This requires a good understanding of the theory of log-schemes and p-adic analytic techniques in arithmetic geometry. The project is a fundamental problem in the study of p-adic cohomology theories. As the theory of log-schemes is well-developed a student who is well-educated in arithmetic geometry should be able to manage this additional difficulty. The successful project will be important and will have applications in integral p-adic Hodge-theory, for example in understanding comparison theorems between de Rham - and p-adic etale cohomology for open varieties. 

The student shall study this paper in the first instance and shall make himself familiar with logarithmic geometry which is a necessary tool to tackle the problem. He should then try and work out the case where the variety is singular and a normal crossing divisor in a regular scheme defined over the ring of Witt vectors. This is a challenging but very interesting problem and many techniques are already well developed and a prototype of this problem (" the good reduction case ") that will allow the student to be able to realize the project.

The student will acquire a lot of expertise in sophisticated techniques in p-adic arithmetic geometry and p-adic Hodge-theory which is really main stream mathematics and internationally highly regarded. At the beginning they will attend courses in the MAGiC consortium, attend workshops and study groups in order to achieve a broader education in areas that may be related but in general go beyond the PhD-topic.

With a completed PhD they will be in a position to apply for Post-Doc positions where in particular the internationally academic market will be available to them and later may find academic positions; in other words the PhD-project prepares the student very well for a University career.

The project is suitable for excellent students who already have a strong background in algebraic or arithmetic geometry.

Funding Minimum
3.5 year studentship: UK/EU tuition fees and an annual maintenance allowance at current Research Council rate. Current rate of £14,296 per year.

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Type / Role:

PhD

Location(s):

South West England