Reduction Mod p of a Finite Group Representation


Jing Yu ( National Taiwan University & Taida Institute for Mathematical Sciences )
2017-03-24  13:30 - 14:30
Room 103, Mathematics Research Center Building (ori. New Math. Bldg.)

Given a finite group G with a prime number p dividing its order. Let (K, A, k) be a modular system (i.e. K is field of char 0 complete w.r.t. a discrete valuation, A is the valuation ring, k is the residue field of char p). Given representation E\' of G over k, we are interested in representation E over K whose reduction mod p is E\'. We will discuss questions relating to the Cartan-Brauer triangles. We will also formulate problems concerning natural Galois representation on P-torsion, E\':=\\phi[P], where \\phi is a rank two Drinfeld F_q[t]-module, and P is a monic irreducible polynomial inside F_q[t].