Secretary of State George Shultz went to Geneva to reopen arms control negotiations with the Soviet Union. Last night he fairly claimed "success." After 14 hours of talks with the Soviet foreign minister, Andrei Gromyko, the two announced that their countries would soon start talking about space and nuclear arms (strategic and intermediate-range) with the ambitious aim of limiting and reducing their arsenals and eventually of eliminating them. So after a frosty 13-month interlude brought on by Moscow's boycott of the START and INF talks, the United States and the Soviet Union will be back at a table.

Each side, it appears, is giving up something to get there. Moscow dropped its rigid and noisy insistence -- the Gorbachev line -- that the American "Star Wars" program be terminated as the first order of arms control business. On its part, the administration seems to have backed off its earlier position, one that was being asserted strongly in the days preceding the Geneva meeting, that it would not even consider submitting "Star Wars" to discussion with Moscow.

The upshot is that space arms will for the first time be included in a negotiation. The discussion of the American Strategic Defense Initiative, of special concern to Moscow, will allow the United States to press its concerns about what Mr. Shultz called "the erosion of the ABM treaty" -- an evident reference to indications of Soviet cheating on that earlier accord. Along with space arms, there will also be talks on strategic and intermediate- range missiles, the familiar categories on which stalemate had already been achieved. This "complex of questions," in the Geneva communiqu,e's phrase, will be taken up by Soviet and American delegations divided into three groups.

There has been no movement in East-West arms control since the Soviets' invasion of Afghanistan in 1979. The labs and the pro have not been similarly inactive. Is there a place now for cautious hope that things are a bit different? Mr. Reagan is resuming negotiations not just because of "peace" pressures, some perhaps self- generated, but because he feels his rearmament program has evened up the bargaining odds. The Soviets appear to have deep anxieties about America's tremendous technological thrust and thus a further incentive to deal.

A formidable backlog of disagreements and difficulties lies in the way of substantive progress. Only the "objectives," not the all-important details of Mr. Reagan's and the Kremlin's negotiating strategies, were pursued at Geneva. Still, it is good to have the two countries engaging again in what Secretary Shultz called "the necessary give and take," and agreeing finally to address the serius issues.