THE INTERSECTION OF THE DIVISION GROUP OF A FINITELY GENERATED
SUBGROUP OF A TORUS WITH AN ALGEBRAIC SUB-VARIETY HAS BEEN UNDERSTOOD
FOR SOME TIME (LANG,LAURENT ..) .AFTER A BRIEF REVIEW OF SOME OF THE TOOLS
IN THE ANALYSIS AND THEIR RECENT EXTENSIONS (ANDRE'-OORT CONJECTURES) ,WE GIVE SOME OLD AND NEW APPLICATIONS;IN PARTICULAR TO THE ADDITIVE STRUCTURE OF THE SPECTRA OF METRIC GRAPHS AND CRYSTALLINE MEASURES.
THE LAST IS JOINT WORK WITH P.KURASOV.