Tautological rings on Jacobian varieties of curves with automorphisms

Anneaux tautologiques sur les variétés Jacobiennes de courbes avec automorphismes

Thomas Richez (1)

1 IRMA - Institut de Recherche Mathématique Avancée

Let J be the Jacobian of a smooth projective complex curve C which admits non-trivial automorphisms, and let ApJq be the ring of algebraic cycles on J with rational coefficients modulo algebraic equivalence. We present new tautological rings in ApJq which extend in a natural way the tautological ring studied by Beauville in [5]. We then show there exist tautological rings induced on special complementary abelian subvarieties of J.

Mots clés: Algebraic cycles; Tautological rings; Jacobians; Automorphisms; Fourier transforms

Domaines: Géométrie algébrique [math.AG]; Anneaux et algèbres [math.RA]

Thomas Richez. Tautological rings on Jacobian varieties of curves with automorphisms. Geometriae Dedicata, 2018, 194 (1), pp.1-28. ⟨10.1007/s10711-017-0262-9⟩. ⟨hal-01899682⟩