セミナー -- Arithmetic Algebraic Geometry Seminars & Lectures
Title
Resolution of nonsingularities for Mumford curves.
Date
December 15 (Thu), 2011, 14:15-15:45
Room
Room 206, RIMS
Speaker
Emmanuel Lepage 氏 (Institut Mathematique de Jussieu)
Abstract
Let $X$ be a hyperbolic curve over $\overline Q_p$. I am interested in the following property: for every semistable model $\mathcal X$ of $X$ and every closed point $x$ of the special fiber there exists a finite covering $Y$ of $X$ such that the minimal semistable model $\mathcal Y$ of $Y$ above $\mathcal X$ has a vertical component above $x$. I will try to explain why hyperbolic Mumford curves satisfy this property. I will give anabelian appplications of this to the tempered fundamental group.
Mini-Workshop ``Rational Points on Modular Curves and Shimura Curves''
Date
Monday, October 26th, 2009
13:30--14:30
Keisuke Arai (Univ. Tokyo)
Points on $X_0^+(N)$ over quadratic fields
(joint work with F. Momose)
Abstract:
Momose (1987) studied the rational points on the modular curve
$X_0^+(N)$ for a composite number $N$. He showed that the rational
points on $X_0^+(N)$ consist of cusps and CM points under certain
conditions on a prime divisor $p$ of $N$. But $p=37$ was excluded.
For $37$ is peculiar because $X_0(37)$ is a hyperelliptic curve and
$w_{37}$ is not the hyperelliptic involution. We show that the
rational points on $X_0^+(37M)$ consist of cusps and CM points.
We also show that the $K$-rational points on $X_0^+(N)$ consist
of cusps and CM points for a quadratic field $K$ under certain
conditions (both $p=37$ and $p\ne 37$ allowed).
14:45--15:45
Fumio Sairaiji (Hiroshima International Univ.)
Takuya Yamauchi (Osaka Prefecture Univ.)
On rational torsion points of central $\mathbb{Q}$-curves
Abstract:
Let $E$ be a central $\mathbb{Q}$-curve over a polyquadratic field $k$.
In this talk we give an upper bound for prime divisors $p$ of the order
of the $k$-rational torsion subgroup of $E$. For example, $p$ is less
than or equal to 13, if the scalar restriction of $E$ from $k$ to
$\mathbb{Q}$ is of GL$_2$-type with real multiplications. Our result
is a generalization of the result of Mazur on elliptic curves over
$\mathbb{Q}$, and it is a precision of the upper bounds of Merel and
Oesterl\'{e}.
16:00--17:00
Pierre Parent (Univ. Bordeaux 1)
Rational points on Shimura curves
Abstract:
For $B$ a rational quaternion algebra, the Shimura curve associated with $B$
(or more precisely its quotient by certain Atkin-Lehner involutions) is a
moduli
space, in a certain sense, for abelian surfaces with potential
multiplication by
$B$. Proving that those curves almost never have rational points would
therefore allow a small step towards the conjecture, attributed to Coleman
and Mazur, which predicts the scarcity of endomorphism algebras for
abelian varieties of GL$_2$-type over $\mathbb{Q}$. We will present
a method to study such rational points, developped by A. Yafaev and myself,
and recently improved by F. Gillibert.
Marco Boggi 氏連続講演
Title
``Profinite curve complexes and the congruence subgroup problem for the mapping class group''
Date
September 27th (Thu) and 28th (Fri), 2007
Room
at Room 206, RIMS, Kyoto University
27th (Thu)
10:00--12:00 Boggi
lunch
14:00--16:00 Boggi
16:00-- free discussion
dinner
28th (Fri)
10:00--12:00 Boggi
lunch
14:00--16:00 free discussion
Abstract
別紙のとおり
Title
Arithmetic from Geometry on Elliptic Curves
Date
June 2 (Fri), 2006, 16:30-17:30
Room
Room 202, RIMS
Speaker
Christopher Rasmussen (Rice Univ.)
Abstract
One of the philosophies of arithmetic geometry made popular by Grothendieck was the notion that the structure of the absolute Galois group of $\mathbf{Q}$, could be determined from geometric (or even combinatoric) data. In a related vein, one finds that the arithmetic properties of a curve are sometimes determined by its geometry. Specifically, the structure of a curve as a cover of the projective line can have arithmetic consequences for the Jacobian of the curve. We will discuss this situation in the case of elliptic curves, where this connection between arithmetic and geometry can be seen very clearly.
Title
Arithmetic Algebraic Geometry Lecture（集中講義）
Date
May 8 (Mon)- May 19, 2006.
Room
こちらをご覧ください
Speaker
加藤和也（京大 理）
Abstract
Weil が 1949 年に提出した Weil 予想は、 1970 年代のはじめに最終的に証明されるまで、 代数幾何学の大きな進展の原動力となり、 とくに Grothendieck が Weil 予想の証明をめざして導入した エタールコホモロジーは、現在の整数論の重要な道具となった。 その経緯をふり返りつつ、エタールコホモロジーの解説をおこなう。
Title
Algebraic dynamical systems (preperiodic points, Mahler measures, equidistribution of small points)
Date
May 1 (Mon), 2006, 16:30-
Room
Room 202, RIMS
Speaker
Lucien Szpiro (City Univ. New York)
Abstract
Reference: (available at http://math.gc.cuny.edu/faculty/szpiro/People_Faculty_Szpiro.html)
--Joint papers with T. Tucker
--Joint paper with E. Ullmo and S. Zhang
Date
April 10 (Mon), 2006, 14:00-17:00
Room
Room 202, RIMS
(14:00-15:15)
Speaker
Michel Matignon (Univ. Bordeaux 1/Chuo Univ.)
Title
Wild monodromy groups and automorphisms groups of curves
(16:00-16:45)
Speaker
Barry Green (Univ. Stellenbosch/Chuo Univ.)
Title
Selected results on liftings of Galois covers of smooth curves from char. p to char. 0