Chronic violence is a growing problem in our society today as evidenced, among other factors, by the ever-increasing murder rate in many of our large urban centers in the United States. Emphasis hasâ€¦ (More)

Ramified primes in the field of moduli. Let f : Y â†’ X = PC be a three point cover, i.e. a finite cover of the Riemann sphere branched at 0, 1 and âˆž. The â€˜obvious directionâ€™ of Belyiâ€™s theorem statesâ€¦ (More)

Let G = Dp be the dihedral group of order 2p, where p is an odd prime. Let k an algebraically closed field of characteristic p. We show that any action of G on the ring k[[y]] can be lifted to anâ€¦ (More)

We study indigenous bundles in characteristic p > 0 with nilpotent p-curvature, and show that they corresponds to simpler objects which we call deformation data. We consider the existence problem ofâ€¦ (More)

The overall aim of this thesis is to compute arithmetic volumes of Shimura varieties of orthogonal type and natural heights of the special cycles on them. We develop a general theory of integralâ€¦ (More)

We study finite groups of automorphisms of the p-adic open disk. In particular, we generalize results of Green, Matignon and Henrio from cyclic groups of order p to arbitrary finite groups. As anâ€¦ (More)

We determine the stable reduction at p of all three point covers of the projective line with Galois group SL2(p). As a special case, we recover the results of Deligne and Rapoport on the reduction ofâ€¦ (More)

In this paper we investigate the cohomological obstruction for the field of moduli of a G-cover to be a field of definition, in the case of local fields and covers with tame admissible reduction.â€¦ (More)

In this paper we study the reduction of Galois covers of curves, from characteristic zero to positive characteristic. The starting point is a recent result of Raynaud, which gives a criterion forâ€¦ (More)