Prime Minister’s Research Fellowship (PMRF)

Our research interests primarily lie in the area of Galois representations.  It is useful to study the representations of absolute Galois group of Q  locally  by restricting it to  the decomposition subgroups at different primes p.  We are interested in  research works related to the mod-p reductions of  2-dimensional local Galois representations attached to modular forms.  These representations are crystalline if the level of the modular form is prime to p. In this case, the results concerning  the structure of modular representations of the general linear group of degree 2 over a finite field plays an important role in the explicit computation of the reduction.