Takao Yamazaki

activity

20052021

most citedReciprocity sheaves

28 citations · 122 across the 26 of their papers we have counts for

collaborators

Showing math.NTShow all

8 papers · 1 filter

math.NT2019

Maximal abelian extension of $X_{0} (p)$ unramified outside cusps

Takao Yamazaki, Yifan Yang

Let $p$ be a prime number. Mazur proved that a geometrically maximal unramified abelian covering of $X_{0} (p)$ over $Q$ is given by the Shimura covering $X_{2} (p) \to X_{0} (p)$ ,…

math.NT2018

Generalized Jacobians of modular and Drinfeld modular curves

Fu-Tsun Wei, Takao Yamazaki

We consider the generalized Jacobian $J$ of the modular curve $X_{0} (N)$ of level $N$ with respect to a reduced divisor consisting of all cusps. Supposing $N$ is square f…

math.NT2016★ 5 cited

Rational torsion on the generalized Jacobian of a modular curve with cuspidal modulus

Takao Yamazaki, Yifan Yang

We consider the generalized Jacobian $J_{0} (N)$ of a modular curve $X_{0} (N)$ with respect to a reduced divisor given by the sum of all cusps on it. When $N$ is a power of…

math.NT2012★ 1 cited

Torsion points on Jacobian varieties via Anderson's p-adic soliton theory

Shinichi Kobayashi, Takao Yamazaki

Anderson introduced a $p$ -adic version of soliton theory. He then applied it to the Jacobian variety of a cyclic quotient of a Fermat curve and showed that torsion points of certai…

math.NT2011

Torsion points on hyperelliptic Jacobians via Anderson's $p$ -adic soliton theory

Yuken Miyasaka, Takao Yamazaki

We show that torsion points of certain orders are not on a theta divisor in the Jacobian variety of a hyperelliptic curve given by the equation $y^{2} = x^{2 g + 1} + x$ with $g \geq 2$ . Th…

math.NT2010★ 3 cited

Brauer-Manin pairing, class field theory and motivic homology

Takao Yamazaki

For a smooth proper variety over a $p$ -adic field, the Brauer group and abelian fundamental group are related to the higher Chow groups by the Brauer-Manin pairing and the class fi…

math.NT2008

Milnor $K$ -group attached to a torus and Birch-Tate conjecture

Takao Yamazaki

We formulate (and prove under a certain assumption) a conjecture relating the order of Somekawa's Milnor $K$ -group attached to a torus $T$ and the value of the Artin $L$ -function a…

math.NT2006

Class field theory for a product of curves over a local field

Takao Yamazaki

We prove that the the kernel of the reciprocity map for a product of curves over a $p$ -adic field with split semi-stable reduction is divisible. We also consider the $K_{1}$ of a pro…

Maximal abelian extension of X0​(p) unramified outside cusps

Generalized Jacobians of modular and Drinfeld modular curves

Rational torsion on the generalized Jacobian of a modular curve with cuspidal modulus

Torsion points on Jacobian varieties via Anderson's p-adic soliton theory

Torsion points on hyperelliptic Jacobians via Anderson's p-adic soliton theory

Brauer-Manin pairing, class field theory and motivic homology

Milnor K-group attached to a torus and Birch-Tate conjecture

Class field theory for a product of curves over a local field

Maximal abelian extension of $X_{0} (p)$ unramified outside cusps

Torsion points on hyperelliptic Jacobians via Anderson's $p$ -adic soliton theory

Milnor $K$ -group attached to a torus and Birch-Tate conjecture