  A fully kinetic Vlasov simulation of the Geospace Environment Modeling (GEM)
Magnetic Reconnection Challenge is presented. Good agreement is found with
previous kinetic simulations using particle in cell (PIC) codes, confirming
both the PIC and the Vlasov code. In the latter the complete distribution
functions $f_k$ ($k=i,e$) are discretised on a numerical grid in phase space.
In contrast to PIC simulations, the Vlasov code does not suffer from numerical
noise and allows a more detailed investigation of the distribution functions.
The role of the different contributions of Ohm's law are compared by
calculating each of the terms from the moments of the $f_k$. The important role
of the off--diagonal elements of the electron pressure tensor could be
confirmed. The inductive electric field at the X--Line is found to be dominated
by the non--gyrotropic electron pressure, while the bulk electron inertia is of
minor importance. Detailed analysis of the electron distribution function
within the diffusion region reveals the kinetic origin of the non--gyrotropic
terms.
