Number Theory and Geometry related to Algebraic Groups

(1)Yukie研究zeta函数与预齐次向量空间，并获得了估计的数量五次领域的判别小于或等于X。(2)花村调查了混合图案，并获得了结果的Kunneth公式的模块化品种。(3)石田建立了一个理论有关的理想理论（环）理性和真实的球迷的环面品种。此外，他发现了一个真实的风扇模拟爆炸的代数品种。特别是对于有限数量的爆破，他证实了与代数簇的相似之处。在代数几何中，Zerkiki-Riemann拓扑可以定义在函数域的赋值环集合上。他定义了这一概念的理性和真实的球迷使用的一套所有添加剂的订单自由模块和真实的向量空间。利用这Zagliki，黎曼拓扑，他证明了存在的紧复曲面品种。(4)Hara推广了环R的理想I的紧闭包的概念， ...更多信息 证明了广义行列式理想τ（I）的各种性质，从而奠定了理论基础。使用这种方法，他适用于证明一个特殊情况下的藤田猜想的全球生成的伴随丛和一个新的证明艾因-拉扎斯菲尔德-史密斯比较定理的符号权力的理想的定期地方环。(5)中村：如果CM椭圆曲线与它的所有伽罗瓦共轭同构，它被称为Q曲线，并具有重要的性质。他分类的所有Q曲线的绝对类领域的一个给定的虚二次领域。众所周知，数域上椭圆曲线的挠群是有限的。他研究如何扭转的变化之间的同源椭圆曲线。(6)Ogata用非常充分的线丛研究了环面簇的投射正规性和定义理想的生成元的度，得到了投射正规性的一些判别准则和定义理想的度的一些估计.少

(1) Yukie investigated zeta functions associated with prehomogeneous vector spaces and obtained an estimate of the number of quintic fields with discriminant less than or equal to X.(2) Hanamura investigated mixed motifs and obtained a result on the Kunneth formula for modular varieties.(3) Ishida established a theory relating ideal theory (of rings) to rational and real fans for toric varieties. Also he found a real fan analogue of blow-ups of algebraic varieties. Especially for a finite number of blow-ups, he confirmed similarities with the case of algebraic varieties. In algebraic geometry, Zariski-Riemann topology can be defined on the set of valuation rings of the function fields. He defined this notion for rational and real fans using the set of all additive orders on free modules and real vector spaces. Using this Zariski-Riemann topology, he proved the existence of the compactification of toric varieties.(4) Hara generalized the notion of tight closure of ideals I of rings R of … More positive characteristic to "I-tight closure" and proved various properties for the generalized determinantal ideal τ(I), thus made a foundation of the theory. Using this method, he applied to the proof of a special case of the Fujita conjecture on the global generation of adjoint bundles and to a new proof of the Ein-Lazarsfeld-Smith comparison theorem on the symbolic power of ideals of regular local rings.(5) Nakamura : If a CM elliptic curve is isogenous to all its Galois conjugate, it is called a Q-curve and has important properties. He classified all Q-curves over the absolute class field of a given imaginary quadratic field. It is well-known that the torsion group of an elliptic curve over a number field is finite. He investigated how the torsion changes among isogenous elliptic curves.(6) Ogata investigated projective normality and the degrees of the generators of the defining ideals of toric varieties by very ample line bundles, and opbtained some criteria of projective normality and some estimates of the degrees of the defining ideals. Less