p-adic Langlands correspondence and Iwasawa theory

Contribution List

7. The Serre filtration on mod p Hilbert modular forms of level p

Fred Diamond

4/24/19, 9:45 AM

A result of Serre relates the space of mod p modular forms of level Gamma_1(Np) and weight 2 to the spaces of mod p modular forms of level Gamma_1(N) and weight between 2 and p+1. I’ll explain a generalization of this to the context of Hilbert modular forms involving a mod p geometric Jacquet-Langlands correspondence. The resulting filtration on mod p Hilbert modular forms of parallel weight...

4. Local-global compatibility and the cohomology of locally symmetric spaces

James Newton

4/24/19, 11:00 AM

I will discuss joint work with Allen, Calegari, Caraiani, Gee, Helm, Le Hung, Scholze, Taylor and Thorne on potential automorphy for certain compatible systems of Galois representations over CM fields. I will particularly focus on the local-global compatibility results needed to establish our automorphy lifting theorems in the ordinary case and explain the application of a key local...

2. An application of a conjecture of Mazur–Tate to supersingular elliptic curves

Emmanuel Lecouturier

4/24/19, 2:00 PM

See the attached document.

12. On extra zeros of p-adic L-functions

Denis Benois

4/24/19, 3:30 PM

See the attached document.

6. Dilogarithm and higher L invariants for GL3(Qp)

Zicheng Qian

4/25/19, 9:45 AM

We consider a semi-stable three dimensional p-adic representation ρ of the absolute Galois group of Qp and assume that ρ has rank two monodromy and is non-critical. It is known that ρ depends on three L invariants up to isomorphism. We construct an explicit family of locally analytic representations of GL3(Qp) depending on three invariants and show that there exists a unique representation...

3. p-adic cohomology of some period domains

Gabriel Dospinescu

4/25/19, 11:00 AM

We will explain how to adapt Orlik's computation of the compactly supported l-adic cohomology of many p-adic period domains (l different from p) to the case l=p. The key input is a vanishing theorem for extensions between generalized Steinberg representations of p-adic reductive groups, with coefficients mod p. This is joint work with Pierre Colmez, Julien Hauseux and Wieslawa Niziol.

8. The eigencurve at Eisenstein weight one points

Alice Pozzi

4/25/19, 2:00 PM

In this talk, we discuss the geometry of the Coleman-Mazur eigencurve at weight one Eisenstein points. The local nature of the eigencurve is mostly understood at classical points of weight greater than one, while one observes some unusual behaviours at weight one. In particular, we study cuspidal Hida families specializing to Eisenstein series at weight one. Our approach consists in studying...

9. Hilbert modular eigenvariety at exotic and CM classical points of parallel weight one

Shaunak Deo

4/25/19, 3:30 PM

We sketch our recent results about the geometry of the p-adic eigenvariety constructed by Andreatta-Iovita-Pilloni, which interpolates Hilbert modular eigenforms over a totally real field F, at classical, regular points of parallel weight one which either are CM or have exotic projective image. To prove these results, we assume the p-adic Schanuel conjecture in most of the cases. The key...

11. On the Hilbert cuspidal eigenvariety at weight one Eisenstein points

Sheng-Chi Shih

4/25/19, 4:45 PM

When the p-adic L-function of a finite order totally odd character \phi of a totally real field F has trivial zeros, any p-stabilization of the corresponding weight one Eisenstein series belongs to the Hilbert cuspidal eigencurve. In the case of elliptic modular forms, it was proved by Betina-Dimitrov-Pozzi that such points are etale over the weight space, hence belong to a unique cuspidal...

5. Norm-compatible cohomology classes in Siegel varieties

Joaquin Rodrigues Jacinto

4/26/19, 9:30 AM

We will explain how to construct towers of interesting classes in the cohomology of Siegel sixfolds. We will study their complex regulator and we will give an application to Iwasawa theory. This is joint work with Antonio Cauchi and Francesco Lemma.

1. Geometry of Siegel eigenvarieties at Saito–Kurokawa points

Adel Betina

4/26/19, 10:45 AM

I will report on joint work with T. Berger studying the geometry of Siegel eigenvarieties. Under certain assumptions we show that they are smooth at points corresponding to Saito-Kurokawa lifts when the tame level is paramodular, but singular when it is Gamma_0(N). Moreover, we give an application to the Bloch-Kato conjecture. Our technique uses pseudorepresentations of p-adic families of...

13. On the geometry of Pappas–Rapoport Shimura varieties

Stéphane Bijakowski

4/26/19, 1:30 PM

After recalling the geometry of the special fiber of the modular curve, I will talk about possible generalizations to Shimura varieties.
I will explain why the situation is more involved when ramification appears, and why one is led to use models defined by Pappas and Rapoport. I will then define an analogous of the ordinary locus in this context.
This is joint work with V. Hernandez.

10. On the density of automorphic points in global deformation spaces

Benjamin Schraen

4/26/19, 3:00 PM

I will discuss the problem of the repartition of automorphic points in global polarized deformation spaces. We can ask the problem in terms of fixed level and varying weight or fixed weight and varying level. I will describe positive answers to these problems and their link with the problem of companion p-adic overconvergent automorphic forms.