Joint IAS/Princeton Arithmetic Geometry Seminar

By an observation of Efimov and Scholze, Efimov's theorem on the rigidity of localizing motives allows one to construct refinements of topological Hochschild homology and its variants. In this talk, I'll explain how this refinement works, sketch an...

Motivated by the instances of Grothendieck’s generalized Hodge conjecture which have a purely algebraic expression, we study the restriction map in cohomology from a smooth projective variety X

to an affine U. Starting from X being defined over an...

A natural problem in the study of local systems on complex varieties is to characterize those that arise in a family of varieties. We refer to such local systems as motivic. Simpson conjectured that for a reductive group G, rigid G-local systems...

A result of Jan Nekovář says that the Galois action on p-adic intersection cohomology of Hilbert modular varieties with coefficients in automorphic local systems is semisimple. We will explain a new proof of this result for the non-CM part of the...

I will explain how several different moduli spaces of bundles on a smooth projective curve have abelian motives. Our starting point is a formula for the motive of the stack of vector bundles on the curve in Voevodsky's category of motives with...

The inverse Galois problem asks for finite group G, whether G is a finite Galois extension of the rational numbers. Malle’s conjecture is a quantitative version of this problem, giving an asymptotic prediction of how many such extensions exist with...

I will talk about a proof of local-global compatibility at p for higher coherent cohomology mod p in weight one for Hilbert modular varieties at an unramified prime, assuming we are not in middle degree. I will discuss some key ingredients to the...

Ohta described the ordinary part of the 'etale cohomology of towers of modular curves in terms of Hida families. Ohta's approach crucially depended on the one-dimensional nature of modular curves. In this talk, I will present joint work with Chris...

The analytic de Rham stack is a new construction in Analytic Geometry whose theory of quasi-coherent sheaves encodes a notion of p-adic D-modules. It has the virtue that can be defined even under lack of differentials (eg. for perfectoid spaces or...

Topology of the Hitchin system has been studied for decades, and interesting connections were found to orbital integrals, non-abelian Hodge theory, mirror symmetry etc. I will explain that a large part of the symmetries in these geometries above are...