STNB2026 (39a edició)
Modular Entanglement
Ponents
Samuele Anni
Resum
We study entanglement phenomena between residual Galois representations attached to modular forms and modular abelian varieties, focusing on whether two such representations—possibly in different residual characteristics—can correspond to the same number field or share a common non-trivial subfield. These questions are closely related to inverse Galois theory and to congruences between modular forms. We present explicit examples arising from elliptic curves: for levels N1,N2 in {3,4,5}, we describe one-dimensional families of pairs of elliptic curves whose N1- and N2-torsion Galois representations exhibit projective A4-entanglement. We also give explicit models for the associated modular surfaces over suitable cyclotomic extensions of Q. This is joint work with David Kohel (AMU) and Zoé Yvon (Toulouse), and ongoing work with Luis Dieulefait (UB) and Gabor Wiese (Université du Luxembourg).
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