On the Bloch–Kato Conjecture for some four-dimensional symplectic Galois representations
Date(s) : 02/09/2025 iCal
14h00 - 15h00
The Bloch–Kato Conjecture predicts a relation between Selmer
ranks and orders of vanishing of L-functions for certain Galois
representations. In this talk, I’ll describe results towards this
conjecture in ranks 0 and 1 for the self-dual Galois representations
that come from Siegel modular forms on GSp(4) with parallel weight (3,
3). The key step is a construction of auxiliary ramified Galois
cohomology classes, which then give bounds on Selmer groups; the
ramified classes come from level-raising congruences and the geometry
of special cycles on Siegel threefolds.
ranks and orders of vanishing of L-functions for certain Galois
representations. In this talk, I’ll describe results towards this
conjecture in ranks 0 and 1 for the self-dual Galois representations
that come from Siegel modular forms on GSp(4) with parallel weight (3,
3). The key step is a construction of auxiliary ramified Galois
cohomology classes, which then give bounds on Selmer groups; the
ramified classes come from level-raising congruences and the geometry
of special cycles on Siegel threefolds.
Emplacement
I2M Luminy - TPR2, Salle de Séminaire 304-306 (3ème étage)
Catégories
