Abstract: Higher codimension Iwasawa theory concerns the support in codimension greater than one of Iwasawa modules. A useful technique when relating this support to p-adic L-functions is to consider the quotient of the top exterior power of an Iwasawa module M of rank r by the sum of the r-th exterior powers of submodules arising from various Panciskin conditions. A natural question is then...

20. Sunsuke YAMANA. On central derivatives of (twisted) triple product p-adic L-functions.

6/24/19, 11:00 AM

Abstract: We will construct twisted triple product p-adic L-functions and discuss its trivial or non-trivial zeros at the center of the functional equation.
In the split and +1 sign case we will determine the trivial zeros of cyclotomic p-adic L-functions associated to three ordinary elliptic curves and identify the double or triple derivatives of the p-adic L-function with the product of the...

21. Antonio LEI. Pseudo-null modules and codimension two cycles for supersingular elliptic curves.

6/24/19, 2:30 PM

Abstract: Let E/ Q be an elliptic curve with supersingular reduction at an odd prime p and a_p(E)=0. Let K be an imaginary quadratic field where p splits and write K_\infty for the compositum of all \mathbb{Z}p-extensions of K. Generalizing Kobayashi's plus and minus Selmer groups over cyclotomic extensions of Q, Kim defined \pm/\pm-Selmer groups for E over K\infty. We present numerical...

22. Florian SPRUNG. Shedding light on Selmer groups for elliptic curves at supersingular primes in Z_p^2-extensions via chromatic Selmer groups.

6/24/19, 4:00 PM

Abstract: We present some results and techniques concerning Selmer groups in Z_p^2-extensions for elliptic curves at supersingular primes, focusing on the case a_p not equal to 0. In this case, a convenient pair of objects to consider is the 'chromatic Selmer groups' (also called 'signed Selmer groups' when a_p=0).

23. Adrian IOVITA. Katz type p-adic L-functions when p is not split in the CM field and applications.

6/25/19, 9:30 AM

Abstract: With F. Andreatta we constructed p-adic L-functions attached to a triple (F, K, p) where F is a classical, elliptic modular eigenform, K a quadratic imaginary field and p a prime integer, all satisfying certain assumptions of which the most important is that p is not split in K. Such p adic L-functions have been constructed by N. Katz (during the 70') if F is an Eisenstein series and...

24. Daniel BARRERA SALAZAR. Triple product p-adic L-functions and Selmer groups over totally real number fields.

6/25/19, 11:00 AM

Abstract: During the nineties Kato obtained deep results on the Birch and Swinnerton-Dyer conjecture in rank 0 for twists of elliptic curves over Q by Dirichlet characters. More recently, Bertolini-Darmon-Rotger and Darmon-Rotger developed analogous methods to treat twists by certain Artin representations of dimension 2 and 4. The aim of this talk is to explain the main ideas of joint ongoing...

25. Mladen DIMITROV. Geometry of the eigencurve and Iwasawa theory.

6/25/19, 2:30 PM

26. Zheng LIU. p-adic families of Klingen-Eisenstein series and theta series.

6/25/19, 4:00 PM

Abstract: p-adic interpolations of Eisenstein series and theta series give explicit examples of p-adic families of automorphic forms. Their congruences with other automorphic forms help show lower bounds of certain Selmer groups. I will first explain the construction of a p-adic Klingen Eisenstein family for symplectic groups, and then discuss its connection with a p-adic family of theta lifts.

38. Poster session

6/25/19, 5:00 PM

27. Jan NEKOVÁŘ. The plectic polylogarithm.

6/26/19, 9:00 AM

Abstract: We are going to describe the Hodge realisation of the plectic polylogarithm and its relation to special values of L-functions. This is a joint work with A.J. Scholl.

28. Guido KINGS. Equivariant motivic Eisenstein classes and a generalization of the Damerell/Shimura/Katz theorem.

6/26/19, 10:15 AM

(joint with J. Sprang).
Abstract: The equivariant polylogarithm allows to construct in a very general setting cohomology classes of arithmetic groups with values in motivic cohomology. Using the regulator to algebraic de Rham cohomology gives interesting algebraic Eisenstein classes. We use this theory to generalize the results of Damerell, Shimura and Katz on the algebraicity of special...

29. Giovanni ROSSO. Families of Drinfeld modular forms.

6/26/19, 11:30 AM

Abstract: Seminal work of Hida tells us that for eigenforms that are ordinary at p we can always find other eigenforms, of different weights, that are congruent to our given form. Even better, it also says that we can find q-expansions whose coefficients are analytic functions of the weight variable k, that when evaluated at positive integers give the q-expansion of classical ordinary...

30. Eric. URBAN. Towards an Euler system for the standard L-function attached to Siegel modular forms.

6/27/19, 9:30 AM

31. Joaquin RODRIGUES JACINTO. Norm-compatible cohomology classes in Siegel varieties.

6/27/19, 11:00 AM

Abstract: 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.

32. David LOEFFLER. p-adic L-functions and Euler systems for GSp(4).

6/27/19, 2:30 PM

Abstract: I will explain how the higher Hida theory recently introduced by Pilloni can be used to construct p-adic L-functions interpolating the criticalvalues of the degree 4 (spin) L-functions of automorphic forms on GSp(4), and the degree 8 L-functions of cusp forms on GSp(4) x GL(2).This is joint work with Vincent Pilloni, Chris Skinner and Sarah Zerbes. I will conclude by describing work...

33. Ryotaro SAKAMOTO. An application of the theory of higher rank Euler, Kolyvagin, and Stark systems.

6/27/19, 4:00 PM

Abstract: Recently, we established the theory of higher rank Euler, Kolyvagin, and Stark systems when a coefficient ring is Gorenstein. In this talk, I will discuss two applications of this theory.First, I will discuss equivariant BSD conjecture. Second, I will outline the construction of a higher rank Euler system for \mathbb{G}_{m} over a totally real field and explain that all higher...

34. Romyar SHARIFI. Eisenstein cocycles in motivic cohomology.

6/28/19, 9:00 AM

Abstract: I will describe joint work with Akshay Venkatesh on the construction of a 1-cocycle on GL_2(Z) valued in a quotient of a limit of second motivic cohomology groups of open subschemes of the square of G_m over Q. I’ll show how the cohomology class of this cocycle is annihilated by an Eisenstein ideal, and I’ll explain how the cocycle specializes to homomorphisms from first homology...

35. Yukako KEZUKA . On the conjecture of Birch and Swinnerton-Dyer for certain elliptic curves with complex multiplication.

6/28/19, 10:15 AM

Abstract: This talk will describe recent joint work in progress with J. Coates, Y. Li and Y. Tian. Let K be the imaginary quadratic field Q(sqrt{-q}), where q is any prime congruent to 7 modulo 16. Let A be the Gross curve defined over the Hilbert class field H of K, with complex multiplication by the ring of integers of K. In their most recent work, Coates and Li found a large family of...

36. Jishnu RAY. Selmer groups of elliptic curves and Iwasawa algebras.

6/28/19, 11:30 AM

Abstract:The Selmer group of an elliptic curve over a number field encodes several arithmetic data of the curve providing a p-adic approach to the Birch and Swinnerton-Dyer, connecting it with the p-adic L-function via the Iwasawa main conjecture. Under suitable extensions of the number field, the dual Selmer becomes a module over the Iwasawa algebra of a certain compact p-adic Lie group over...

37. Opening

Choose timezone

Iwasawa 2019