V
主页
芝加哥大学数学系座谈会:My Favorite Algebraic Cycle(2021.2.17)
发布人
https://m.youtube.com/watch?v=X1o8BP-rwmI&list=PLXOaY9trlJU08es-H2wx3sY0D3IltSP7e&index=8 Spencer Bloch (University of Chicago) Abstract: Hasse Weil L-functions L(H^n(X),s) are functions of a complex variable s, analytic in a half-plane, associated to an algebraic variety X defined over Q (or more generally any number field), together with a choice of cohomological degree n. They have an Euler product expansion with local factors at good reduction primes p of the form (f_p = geometric frobenius at p) 1/det(1-f_pp^{-s}|H^n(X_{\F_p})). The simplest is the Riemann zeta function. Another example is L(H^1(E),s) with E an elliptic curve. Significant progress has been made in understanding these in recent years due to the introduction of Euler systems by Kolyvagin and Kato. The basic conjecture (first formulated by Birch and Swinnerton-Dyer, and then greatly generalized by Beilinson) is that the behavior of L at integer values of s should be controlled by algebraic cycles. I will focus on the case dim X = 2m-1 is odd, and n=2m-1. The order of vanishing of L(H^{2m-1}(X),s) at s = m is then conjectured to be the rank of the Chow group of codim m algebraic cycles homologous to 0 modulo rational equivalence on X, CH^m(X)^0. For example, when dim X=1, this becomes the Mordell-Weil group of 0-cycles on X of degree 0 modulo divisors of functions. The order of 0 at s=1 should be the rank of the Mordell-Weil group, and the value of the first non-vanishing term in the Taylor series expansion of L(H^1(X),s) in s at s=1 should be given upto elementary factors by the discriminant of the height pairing on the Mordell Weil group. Not much is known in the case dim X=2m-1 1. The talk will focus on a class of elementary examples of varieties X and cycles Z. The construction is geometric rather than arithmetic, and there are interesting links with hypergeometric motives and limiting mixed Hodge structures.
打开封面
下载高清视频
观看高清视频
视频下载器
芝加哥大学数学系座谈会:Homology Growth in Towers and Aspherical Manifolds(2020.10.21)
芝加哥大学数学系座谈会:Quantum Symmetry(2021.5.12)
17课:老子道论的哲学本质
芝加哥大学数学系座谈会:Exotic Calabi-Yau Metrics(2021.1.27)
芝加哥大学数学系座谈会:Liouville Quantum Gravity as a Metric Space and a Scaling Limit
黄煌 经方应用经验20条
Jean-Pierre Serre塞尔的数学回忆 3P 洛桑联邦理工大学Bernoulli中心EPFL 2022
讲座回看:SCI 论文写作与优化精要
ICM2014首尔国际数学家大会数学45分钟特邀演讲(1):韩琦/知识与力量:康熙时期(1662-1722)中欧数学传播的社会史
【九上数学】配方法解一元二次方程
杨振宁先生谈“我的学习经历”
卡尔萨根Carl Sagan圣诞日讲演 Christmas lectures 1977
【九上数学】二次函数与方程
【线性代数】新定义:矩阵的性质P(高三及以上可看)
2024高联代数自然理解
2022年阿贝尔奖颁奖典礼(2022.5.24)Dennis Sullivan
1.3-【国科大本科生课程】代数·李文威老师(20170911录制)
【公开课】《三角学》
2017年第五届纪念吴大猷物理科学讲座:Kip Thorne/利用引力波探索宇宙:从宇宙大爆炸到黑洞 密歇根大学(2017.9.13)
2018年第六届纪念吴大猷物理科学讲座:Duncan Haldane/拓扑量子物质、量子纠缠与“第二次量子革命” 密歇根大学
[开放课程]矩阵分析 32P 授课老师 吴培元
[中字]纪录片-拉格朗日
【精校】巴菲特最具代表性商学院讲座| 乔治亚大学特里商学院 2001.7.18 【中英】
我的大学生活(1972)在罗蒙诺索夫国立莫斯科大学学习
【线性代数】新定义:奇数阶方阵的φt变换(高三及以上可看)
CMI克雷数学研究所20周年纪念会议 10P(2018.9.24-26)
简析2024高联二试第一题!
沐神在交大讲座全过程
[开放课程]变分学导论 25P 授课老师 林琦焜
李群李代数-1
Valendimir Arnold阿诺德Острова电视节目
ICM2014首尔国际数学家大会-数学教育及数学普及45分钟特邀演讲 2P(2014.8.20)
KIAS韩国高等研究院 宇宙学基础 by Viatcheslav Mukhanov 6P(2019.3.29)
阿卜杜斯-萨拉姆Abdus Salam诞辰90周年纪念会议(2016.1.25-28)36P NTU南洋理工大学-ICTP国际理论物理中心
Steven Weinberg 温伯格演讲:终极理论之梦(2014.1.15)
给你平方和立方,求一次方?代数经典
阿布里科索夫Abricosov的生平与科学 2003年诺贝尔物理学奖
KIAS韩国高等研究院弦理论讲座D-instanton amplitudes in String Theory with Ashoke Sen 3P
数学149分爸爸癌症晚期,张雪峰破例为考生亲自报考
钱致榕、王贻芳、陈平 | 今天如何办一所理想的大学?《敢为天下先:三年建成港科大》新书分享会