p-adic methods in arithmetic geometry at Sendai,
2016
2016 October 31–November 2
Tohoku University, Katahira campus, Tokyo Electron House of creativity
Lecture Room in 3rd Floor

Program
October 31, Monday
10:00–12:00

Free discussion

Lunch Break(Kyushu Univ.)
14:00–15:00 Shin HATTORI
On a properness of the Hilbert eigenvariety at integral weights
Coﬀee Break(Osaka Univ.)
15:45–16:45 Seidai YASUDA
Belyi’s theorem in characteristic two
November 1, Tuesday(Tohoku Univ.)
11:00–12:00 Masataka CHIDA
Comparison of periods and R = T theorems
Lunch Break(Univ. of Tokyo)
13:30–14:30 Yoichi MIEDA
Cohomology of aﬃnoid perfectoid spaces and their reductions(Chuo Univ.)
14:45–15:45 Kanetomo SATO
Cycle complex and motivic cohomology extended by zeroCoﬀee Break(Université Paris 8)
16:30–17:30 Abdellah MOKRANE
A rigid version of the Nagata-Zariski purity theorem
Conference Dinner
November 2, Wednesday(Tohoku Univ.)
10:00–11:00 Tomomi OZAWAClassical weight one Hilbert cusp forms in a Hida family
Coﬀee Break(Kyushu Univ.)
11:15–12:15 Shinichi KOBAYASHI
Iwasawa theory on generalized Heegner cycles at non-ordinary primes
Lunch BreakFreediscussion
14:00–17:30
This workshop is supprted by “Japan Society for the Promotion of Science, Program for Advancing Strategic International Networks to Accelerate the Circulation of Talented Researchers”,“Tohoku Forum for creativity (Tohoku University)”, and “Grant-in-Aid for Young Scientists (A)
16H05993”.
Organizers: Nobuo Tsuzuki, Tomoyuki Abep-adic methods in arithmetic geometry at Sendai,
2016
Abstracts
Masataka CHIDA: Comparison of periods and R = T theorems
The comparison of several periods of automorphic forms is important in Iwasawa theory. In
this talk, we will explain a result on the comparison between Hida’s canonical period of elliptic
modular forms and the period of quaternionic automorphic forms in the low weight crystalline
case using R = T theorem. This is based on a joint work with Ming-Lun Hsieh.
Shin HATTORI: On a properness of the Hilbert eigenvariety at integral weights
Let p be a rational prime and G a reductive algebraic group over Q. The eigenvariety for G is arigid analytic variety which p-adically interpolates Hecke eigensystems of finite slopes appearing
in the space of automorphic forms of a fixed tame level on G. Though it plays an importantrole in number theory, its geometry is not well-understood yet. In this talk, I will explain how
to show a properness of Andreatta-Iovita-Pilloni’s eigenvariety of Hilbert cuspidal eigenforms at
integral weights for some cases, using the theory of canonical subgroups of abelian varieties.
Shinichi KOBAYASHI: Iwasawa theory on generalized Heegner cycles at non-ordinary primes
We explain the Iwasawa theory on generalized Heegner cycles comparing to the classical cyclotomic theory via cyclotomic units. For ordinary primes, such an approach was known (cf.
Castella-Hsieh). In this talk, we give a unified treatment including the non-ordinary case.
Yoichi MIEDA: Cohomology of aﬃnoid perfectoid spaces and their reductions
Under some conditions, I will compare the ℓ-adic cohomology of an aﬃnoid perfectoid space
and that of the reduction of its formal model. I will also give some applications to the local
Langlands correspondence.
Abdellah MOKRANE: A rigid version of the Nagata-Zariski purity theorem
After recalling the classical Nagata-Zariski purity theorem and the outline of the proof following
SGA 2, we give a rigid version of this theorem. We extend this version to some cases where thecodimension condition is not satisfied. Finally we explain how to apply this results to the p-adic
monodromy of the moduli space of ordinary abelian varieties.
Tomomi OZAWA: Classical weight one Hilbert cusp forms in a Hida family
Let F be a totally real field and p an odd prime. We consider a primitive p-ordinary Hida family
F of parallel weight Hilbert cusp forms defined over F . It is known that a specialization of Fat any arithmetic points of weight at least two is a classical Hilbert cusp form. However, this is
not always the case for weight one specializations. Balasubramanyam, Ghate and Vatsal provedthat such a Hida family admits infinitely many classical weight one specializations if and only
if it is of CM type. In this talk, for a non-CM primitive p-ordinary Hida family F, we give anexplicit estimate on the number of classical weight one specializations of F.

Kanetomo SATO: Cycle complex and motivic cohomology extended by zero
Motivic cohomology with compact support for varieties over a field is defined by FriedlanderVoevodsky about 20 years ago. In this talk, we give an alternative approach to define motivic
cohomology of smooth varieties using cycle complexes extended by zero. We will also give acomparison result between our construction and the construction of Friedlander-Voevodsky insome special case.
Seidai YASUDA: Belyi’s theorem in characteristic two
Belyi’s theorem states that, for a smooth projective curve X over the field C of complex numbers,
X is defined over a number field if and only if there exists a finite morphism from X to theprojective line over C which is unramifield outside {0, 1, ∞}. An analogue of this statement overan algebraically closed field of characteristic p > 0 was proposed by Mohamed Saı̈di and wasproved by him when p is odd. In this talk, a proof in the remaining case is discussed. This talkis based on my joint work with Yusuke Sugiyama.