Organizers: Tomoyuki Abe (Kavli IPMU, University of Tokyo), Wataru Kai (Tohoku University), Atsushi Shiho (University of Tokyo), Nobuo Tsuzuki (Tohoku University)

18 August (Monday)

11:30--12:30, Christopher Frei, "Hasse principle for 100% of diagonal cubic bundle surfaces"

Lunch

14:00--15:00, Yasuhiro Oki, "Hasse norm principle for extensions of prime squared degree"

Coffee

15:30--16:30, Yuta Suzuki, "Telhcirid's theorem on arithmetic progressions"

Conference dinner (contact Kai kaiw-at-tohoku.ac.jp beforehand)

19 August (Tuesday)

10:00--11:00, Takato Watanabe, "On p-adic Galois representations of monomial fields and p-adic differential modules on fake annuli"

Coffee

11:30--12:30, Bruno Chiarellotto, "The tempered tube and the tempered cohomology"

Lunch

14:00--15:00, Yuanmin Liu, "p-adic weight spectral sequences of strictly semi-stable schemes over formal power series rings via arithmetic D-modules"

Coffee

15:30--16:30, Shigeki Matsuda, "Generalized Witt vectors and its applications"

Monday

Christopher Frei

Hasse principle for 100% of diagonal conic bundle surfaces

We prove that 100% of diagonal conic bundle surfaces over the rational numbers satisfy the Hasse principle, i.e. they have rational points whenever they have real and p-adic points for all primes p.

Lunch break

Yasuhiro Oki

Hasse norm principle for extensions of prime squared degree

Hasse norm principle is one of the classic problems in algebraic number theory, which measures the gap between global and local norms attached to finite separable field extensions of global fields. It is known that the Hasse norm principle may or may not hold in general. Hence, it is natural to investigate an equivalence condition for the validity of the Hasse norm principle with respect to extensions of degree a given positive integer $d$. This problem has been fully resolved in the cases that $d$ is a prime number and $d \leq 15$. In other cases, there exist numerous partial results, but a complete solution has not yet been found. In this talk, we discuss the above question when $d$ is a prime squared.

Yuta Suzuki

Telhcirid's theorem on arithmetic progressions

The classical Dirichlet theorem on arithmetic progressions states that there are infinitely many primes in a given arithmetic progression

with a trivial necessary condition. In this talk, we prove a reversed version of this theorem, which may be called Telhcirid's theorem on arithmetic progressions, i.e., we prove that for any base, there are infinitely many primes whose reverse of digital representation is in a given arithmetic progression, except some degenerate cases. This talk is based on joint work with Gautami Bhowmik (University of Lille).

Tuesday

Takato Watanabe

On p-adic Galois representations of monomial fields and p-adic differential modules on fake annuli

Monomial fields are generalizations of Laurent series fields over fields of characteristic $p$, and they appear in Kedlaya's proof of the semistable reduction theorem for overconvergent $F$-isocrystals. Analogous to the relation between Q_p and F_p ((t)), certain $p$-adic fields can be associated with monomial fields. We study some $p$-adic Galois representations of both monomial fields and their associated $p$-adic fields by constructing and analyzing $p$-adic differential modules on fake annuli.

Bruno Chiarellotto 

The tempered tube and the tempered cohomology

We will discuss a recent joint work with F. Bambozzi and P. Vanni (https://arxiv.org/abs/2410.09473). In the derived analytic spaces in the non arch. setting there are opens where the sections not only converge but they have also some arithmetic properties (log-growth). We will discuss how to construct such spaces  and we will give some applications: to the classical log-growth trasfer theorem and  on a new interpretation of convergent cohomology  where one can replace the classical tube of the rigid cohomology  with a "tempered one".

Lunch break

Yuanmin Liu

p-adic weight spectral sequences of strictly semi-stable schemes over formal power series rings via arithmetic D-modules

Over the Laurent series field k((t)), Lazda–Pál defined the E†-valued rigid cohomology and Caro constructed the theory

of arithmetic D-modules. These p-adic cohomology and its coefficients theory contain more information of varieties over

k((t)) compared to Berthelot’s classical theory of E-valued rigid cohomology or arithmetic D-modules. In this talk, I will

introduce the construction of weight spectral sequence using the theory of arithmetic D-modules, which is an example of

how E†-valued p-adic cohomology reflects the geometry of varieties over k((t)).

Shigeki Matsuda

Generalized Witt vectors and its applications

Classical theory of Witt vectors was generalized by Hazewinkel around 1980's to the case of ramified base and with Frobenius twist, which corresponds to twisted Lubin-Tate groups.  Several years ago, the author generalized his constuction to a little bit more general commutative one-dimensional formal groups, and using this, generalized π-exponentials. In this talk, we give two applications of generalized Witt vector theory. First one is a generalization of the p-adic entire function defined by F. Baldassarri. Second one is a generalization of analytic form of additive character (called "splitting function" in Dwork's paper). This can be also regarded as a p-adically analytic expression of division points of one-dimensional commutative formal groups.