We study the stack of quasi-deRham (\phi,\Gamma)-modules. And use this to construct and then study the so called paraboline varieties, which generalize people's work on the trianguline varieties. On the automorphic side, We construct relative eigenvarieties, and prove the existence of some local-global compatible morphisms between them via showing the density of "classical points". Zoom link = https://wwu.zoom.us/j/62084376529?pwd=ajZnNndIdGdpNWVleFVsdk9ibFRuZz09 Meeting ID: 620 8437 6529, Passcode: 831811