000149801 001__ 149801 000149801 005__ 20251017144645.0 000149801 0247_ $$2doi$$a10.1515/forum-2017-0008 000149801 0248_ $$2sideral$$a142201 000149801 037__ $$aART-2018-142201 000149801 041__ $$aeng 000149801 100__ $$aElias, Yara 000149801 245__ $$aCM cycles on Kuga–Sato varieties over Shimura curves and Selmer groups 000149801 260__ $$c2018 000149801 5060_ $$aAccess copy available to the general public$$fUnrestricted 000149801 5203_ $$aGiven a modular form f of even weight larger than two and an imaginary quadratic field K satisfying a relaxed Heegner hypothesis, we construct a collection of CM cycles on a Kuga–Sato variety over a suitable Shimura curve which gives rise to a system of Galois cohomology classes attached to f enjoying the compatibility properties of an Euler system. Then we use Kolyvagin’s method, as adapted by Nekovář to higher weight modular forms, to bound the size of the relevant Selmer group associated to f and K and prove the finiteness of the (primary part) of the Shafarevich–Tate group, provided that a suitable cohomology class does not vanish. 000149801 540__ $$9info:eu-repo/semantics/openAccess$$aby-nc-nd$$uhttps://creativecommons.org/licenses/by-nc-nd/4.0/deed.es 000149801 590__ $$a0.867$$b2018 000149801 591__ $$aMATHEMATICS$$b120 / 313 = 0.383$$c2018$$dQ2$$eT2 000149801 591__ $$aMATHEMATICS, APPLIED$$b170 / 254 = 0.669$$c2018$$dQ3$$eT3 000149801 592__ $$a0.898$$b2018 000149801 593__ $$aMathematics (miscellaneous)$$c2018$$dQ1 000149801 593__ $$aApplied Mathematics$$c2018$$dQ1 000149801 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/acceptedVersion 000149801 700__ $$0(orcid)0000-0003-3673-3620$$ade Vera-Piquero, Carlos 000149801 773__ $$g30, 2 (2018), 321-346$$pForum math.$$tForum mathematicum$$x0933-7741 000149801 8564_ $$s294613$$uhttps://zaguan.unizar.es/record/149801/files/texto_completo.pdf$$yPostprint 000149801 8564_ $$s1448365$$uhttps://zaguan.unizar.es/record/149801/files/texto_completo.jpg?subformat=icon$$xicon$$yPostprint 000149801 909CO $$ooai:zaguan.unizar.es:149801$$particulos$$pdriver 000149801 951__ $$a2025-10-17-14:33:42 000149801 980__ $$aARTICLE