Program & Schedule

Schedule of the workshop

Saturday - July 4, 2026
10:00-11:00	Shinichi Kobayashi	p-adic aspects of the coefficients of the Weierstrass sigma function at supersingular primes
11:15-12:15	Francesc Castella	On Kato's main conjecture for non-ordinary modular forms
12:30-14:00	--	Lunch Break
14:00-15:00	Zheng Liu	Yoshida lifts and congruences
15:15-16:15	Yuanqing Cai	Branching problems for non-linear covering groups
16:30-17:30	Jie Lin	Deligne’s conjecture for Rankin-Selberg L-functions over CM-fields [online]
18:30--	--	Reception (registration required)
Sunday - July 5, 2026
10:00-11:00	Benjamin Collas	Stack homotopy geometry: arithmetic and anabelian aspects
11:15-12:15	Naoki Imai	TBA
12:30-14:00	--	Lunch Break
14:00-15:00	Fabien Trihan	On the ramified Iwasawa Main Conjecture for elliptic curves over function field of characteristic p>0.
15:15-16:15	Masato Kurihara	Selmer groups and Kolyvagin systems
16:30-17:30	Vladimir Dokchitser	Reduction types of curves of genus 2 [online]

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Titles and Abstracts

Yuanqing Cai, Hokkaido University

Title: Branching problems for non-linear covering groups

Abstract: How does an irreducible representation of a group decompose when restricted to a subgroup? This question lies at the heart of branching problems, a fundamental topic in representation theory with deep connections to other areas of mathematics.

For reductive groups, the relative Langlands program predicts hidden structures underlying such problems. However, much less is known for non-linear covers of reductive groups. In this talk, we discuss several examples of branching problems for covering groups, with particular emphasis on multiplicity-free restrictions.

Francesc Castella, UC Santa Barbara

Title: On Kato's main conjecture for non-ordinary modular forms

Abstract: In the early 1990s Kato formulated a generalised Iwasawa main conjecture for motives. In this talk, after discussing some motivation coming from applications to the Birch and Swinnerton-Dyer conjecture and generalisations, I will explain recent progress on Kato's main conjecture for modular forms at non-ordinary primes based on joint work with Zheng Liu and Xin Wan.

Benjamin Collas, RIMS, Kyoto University

Title: Stack homotopy geometry: arithmetic and anabelian aspects

The homotopy theory of algebraic spaces, through their étale fundamental groups, reveals new arithmetic properties of number fields and p-adic fields, either as invariants arising from moduli phenomena or as base fields in anabelian reconstructions. In this talk, we discuss these themes from the perspective of algebraic stack.

We first apply stack-theoretic methods to Oda's problem -- concerning the invariance of stabilizing number fields generated from the Galois action on the moduli spaces of curves as their genus and number of marked points varies (a setting related to Ihara's question and the Rasmussen-Tamagawa conjecture). We then present how stack considerations establish the Grothendieck conjecture for Deligne-Mumford curves beyond the classical hyperbolicity setting.

Time permitting, we will conclude with recent directions of research of potential interest for algebraic number theorists: some new kind of fields (namely, Kummerfaithful fields) and the ``mono-analycity vs arithmetic holomorphic'' anabelian principles.

This talk includes joint work with S. Philip and N. Yamaguchi.

Vladimir Dokchitser, UCL, online

Title: Reduction types of curves of genus 2

Abstract: During the days of early experiments on the Birch--Swinnerton-Dyer conjecture, Tate produced a table for elliptic curves over p-adic fields that beautifully summarises their arithmetic invariants. I will present an analogous set of tables for curves of genus 2. The invariants addressed include: reduction type of the minimal regular model, Neron component group of the Jacobian, conductor exponent, and the valuation of the discriminant of a minimal Weierstrass model. This is joint work with Edwina Aylward, Lilybelle Cowland Kellock and Elvira Lupoian.

Naoki Imai, University of Tokyo

TBA

Shinichi Kobayashi, Kyushu University

Title: p-adic aspects of the coefficients of the Weierstrass sigma function at supersingular primes

Abstract: The coefficients of the Weierstrass sigma function are interesting objects related to special values of Eisenstein series. In particular, for CM elliptic curves, their squares express special values of the L-function associated with the anticyclotomic deformation of the corresponding Hecke character. Thus, their p-adic properties are closely related to the existence of p-adic L-functions.

When p is ordinary, the p-adic properties of these coefficients have long been understood. In the supersingular case, the speaker, together with Kenichi Bannai and Seidai Yasuda, previously determined lower bounds for the p-adic valuations of the coefficients and the radius of convergence. Motivated by recent developments concerning Iwasawa theory for CM elliptic curves at inert primes, the speaker has obtained more refined estimates and congruence relations. Time permitting, the speaker will also discuss a supercongruence among special values of Eisenstein series at supersingular points obtained in connection with this problem.

Masato Kurihara, Keio University

Title: Selmer groups and Kolyvagin systems

Abstract: I will discuss the structure of Selmer groups of self-dual Galois representations over number fields, using several zeta elements, especially Kolyvagin systems of rank 0 (or Gauss sum type). The most typical example is the classical Selmer group of an elliptic curve over Q, which we will explain in detail. This is joint work with Ryotaro Sakamoto.

Jie Lin, Universität Duisburg-Essen, online

Title: Deligne’s conjecture for Rankin-Selberg L-functions over CM-fields

Abstract: In this talk, we shall first introduce Deligne's conjecture for critical L-values which generalizes the fact that for a positive integer m, \(\zeta(2m)\) is a rational multiple of \((2\pi i)^{2m}\). We will then refine Deligne's conjecture for Rankin-Selberg L-functions over CM fields. In the end, we will introduce a new strategy to prove this conjecture. This is joint work with Harald Grobner, Michael Harris, and A. Raghuram.

Zheng Liu, UC Santa Barbara

Title: Yoshida lifts and congruences

Abstract: A Yoshida lift is the theta lift of two modular forms to GSp(4). Its congruence with stable forms on GSp(4) can be used to produce a lower bound on the Selmer group of the Rankin-Selberg product of the two modular forms. We study this congruence by using Rallis inner product formula, Bessel periods and Furusawa’s pullback formula, together with p-adic interpolation.

Fabien Trihan, Sophia University

Title: On the ramified Iwasawa Main Conjecture for elliptic curves over function field of characteristic p>0.

Abstract: Let $A/K$ be an ordinary semistable elliptic curve over a global function field of characteristic $p>0$, and let $L/K$ be a $\mathbf Z_p^d$-extension ramified at only finitely many places where $A$ has ordinary or multiplicative reduction. We study the Iwasawa main conjecture for such ramified extensions, relating the characteristic ideal of the dual Selmer group over $L$ to a multivariable $p$-adic $L$-function. The main new ingredient is a $\chi$-formula comparing $\chi$-isotypic characteristic ideals with suitable specializations of the $p$-adic $L$-function. Combined with functional equations and specialization and restriction formulae, this yields the main conjecture under a natural $\mu$-minimality hypothesis detectable on the unramified line.