Schubert varieties are known to be Frobenius split in positive
characteristic by the work of Mehta and Ramanathan. More recently,
Bhatt showed that the full flag variety for GLn
is a splinter by entirely different methods. In this talk, we
will...
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...
