Place: MCM110
Title: TBA
Abstract: TBA
Speaker: Prof. Thomas J. Haines (University of Maryland)
Place: MCM110
Title: TBA
Abstract: TBA
Speaker: Prof. Huayi Chen (Westlake University)
Place: MCM110
Title: TBA
Abstract: TBA
Speaker: Prof. Haining Wang (Fudan University)
Place: MCM110
Title: TBA
Abstract: TBA
Speaker: Prof. Chia-Fu Yu (Institute of Mathematics, Academia Sinica of Taiwan)
Place: MCM110
Title: On the supersingular locus of Shimura varieties for quaternionic unitary groups
Abstract: We study a Shimura variety attached to a unitary similitude group of a skew-Hermitian form over a totally indefinite quaternion algebra over a totally real number field. We give a necessary and sufficient condition for the existence of skew-Hermitian self-dual lattices, and show that the superspecial locus in the fiber at p of the associated Shimura variety is non-empty. We also give an explicit formula for the number of irreducible components of the supersingular locus when p is odd and unramified in the quaternion algebra. This talk is the joint work with Yasuhiro Terakado and Jiangwei Xue.
Place: MCM110
Title: TBA
Abstract: TBA
Place: MCM110
Title: TBA
Abstract: TBA
Place: MCM110
Title: 奇亏格超椭圆曲线的局部整体原则
Abstract: Scharaschkin和Skorobogatov等人猜测Brauer-Manin障碍是定义在数域上的射影光滑曲线上的有理点不满足局部整体原则的唯一障碍。对于任意数域和任意给定奇自然数g,我们具体构造出无穷条亏格为g的由Brauer-Manin障碍解释的局部整体原则失效的曲线。我们的结论为上述猜想给出了具体的例证。这是我指导的博士生黄凯最近的工作。
Speaker: Prof. Meng Fai Lim (Central China Normal University)
Place: MCM110
Title: On fine Selmer groups
Abstract: The fine Selmer group has been a much studied object in Iwasawa theory. One of its original roles was to provide a means of formulating (and proving) the main conjecture. On the other hand, the work of Coates and Sujatha initated a systematic study on this group on its own right. My talk will focus on this latter aspect. I shall begin with giving a brief survey on the work of Coates-Sujatha. After that, I will then report some of my work on the following two themes.
(1) A torsioness conjecture on the fine Selmer group over an arbitrary Zp-extension.
(2) A question of Greenberg concerning an explicit description of the structure of the fine Selmer group over the cyclotomic Zp-extension of Q and formulation of its variants.