ar X iv : 0 90 6 . 27 53 v 1 [ m at h . G N ] 1 5 Ju n 20 09 Arcs in the Plane ∗

ar X iv : 0 90 6 . 18 57 v 1 [ m at h . C O ] 1 0 Ju n 20 09 On the circumference , connectivity and dominating cycles

Every 4-connected graph with minimum degree δ and connectivity κ either has a cycle of length at least 4δ − 2κ or has a dominating cycle.

ar X iv : 0 90 6 . 32 38 v 1 [ m at h . N T ] 1 7 Ju n 20 09 GEOMETRIC AND p - ADIC MODULAR FORMS OF HALF - INTEGRAL WEIGHT by Nick

ar X iv : 0 90 6 . 48 35 v 1 [ m at h . O C ] 2 6 Ju n 20 09 The Complex Gradient Operator and the CR - Calculus

ar X iv : 0 90 1 . 18 06 v 1 [ m at h . A G ] 1 3 Ja n 20 09 GREENBERG APPROXIMATION AND THE GEOMETRY OF ARC SPACES

We study the differential properties of generalized arc schemes and geometric versions of Kolchin’s Irreducibility Theorem over arbitrary base fields. As an intermediate step, we prove an approximation result for arcs by algebraic curves.

ar X iv : 0 90 6 . 32 55 v 1 [ m at h . N T ] 1 7 Ju n 20 09 THE OVERCONVERGENT SHIMURA LIFTING by Nick Ramsey

— We construct a rigid-analytic map from the the author’s half-integral weight cuspidal eigencurve (see [10]) to its integral weight counterpart that interpolates the classical Shimura lifting.