Alladi Ramakrishnan Hall

A question on equivariant vector bundles in positive characteristics

Rohith Varma

Let X be a smooth projective curve over an algebraically closed field k and G a finite subgroup of its automorphism group. We denote by Y the curve X/G. Given a G equivariant vector bundle E on X, following ideas from a paper by I. Biswas, we can associate (functorial) a parabolic vector bundle on Y, call it F. Unlike the case of curves over complex numbers, when the field has positive characteristics, this association is not in general an equivalence of the respective categories. But still out of mathematical curiosity, one can look for relations between natural invariants attached to E and F, for example one may try to look for relations between the degree of E and the Parabolic degree of F. The aim of the talk is to discuss some of the issues that arise in the above context. If time permits I will explain the case of weakly ramified covers where a reasonably nice relation can be derived between the degree of E and the parabolic degree of F.