Arithmetic and Diophantine Geometry, via Ergodic Theory and o-minimality

Session

Afternoon Chair: Jonathan Pila

11 sept. 2025, 14:00

Centre de conférences Marilyn et James Simons (Le Bois-Marie)

16. Proportionality and the Arithmetic Volumes of Shimura Varieties and the Moduli of Shtukas

Wei Zhang (MIT)

11/09/2025 14:00

The volume of a locally symmetric space is essentially a product of special values of zeta functions. More generally, Hirzebruch's proportionality theorem (extended by Mumford) tells us how to integrate any Chern class polynomial on a locally symmetric space. We prove an analog and extension of these results to function fields, where locally symmetric spaces will be replaced by the moduli...

17. On the Bloch–Kato Conjecture for Some Four-Dimensional Symplectic Galois Representations

Naomi Sweeting (Princeton Univ.)

11/09/2025 15:15

The Bloch–Kato Conjecture predicts a relation between Selmer ranks and orders of vanishing of L-functions for Galois representations arising from etale cohomology of algebraic varieties. 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); these contribute...