Abstract submitted to the International Europhysics Conference on High Energy Physics July 12 - 18, 2001, Budapest, Hungary _________________________________________________________________________ Inclusive jet cross sections in neutral current deep inelastic scattering in the Breit frame and determination of alpha_s at HERA ZEUS Collaboration Abstract Inclusive jet differential cross sections for the reaction e^+p -> e^+ + jet(s) + X have been measured in neutral current interactions at Q^2 > 125 GeV^2 with the ZEUS detector at HERA using an integrated luminosity of 38 pb^{-1}. Jets are identified in the Breit frame using the longitudinally invariant k_T-cluster algorithm. Measurements of differential inclusive jet cross sections are presented as functions of the jet transverse energy, E_Tjet^b, jet pseudorapidity, eta_jet^b, jet azimuthal angle, phi_jet^b, and Q^2 for jets with E_Tjet^b > 8 GeV. Next-to-leading-order QCD calculations give a good description of the measurements at high Q^2 or high E_Tjet^b. The measured azimuthal distribution is non-uniform. Its shape is well described by the QCD prediction. A QCD analysis of the measured inclusive jet cross sections at high Q^2 or high E_Tjet^b allows a precise determination of alpha_s(M_Z) and a detailed estimate of the uncertainties of the NLO QCD predictions arising from the parton distribution functions of the proton. The value of alpha_s(M_Z), as determined from the QCD fit to dsigma/dQ^2 for Q^2 > 500 GeV^2, is alpha_s(M_Z) = 0.1190 \pm 0.0017 (stat.) ^{+ 0.0049}_{- 0.0023} (syst.) ^{+ 0.0026}_{-0.0026} (th.).