作者studentkuo (sk)
看板NTU-MSA
标题[宣传] Frans Oort的演讲(为学生举办)
时间Tue Nov 27 22:24:44 2012
我们有机会邀请任教於乌特勒支大学的Frans Oort教授，为研究所及大学部，提供两场学
术性质的演讲，欢迎大家参与。主题请见下方。
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Speaker: Frans Oort (University of Utrecht)
Time: December 7 (Friday), 4 - 5:30 pm
Place: Room 101
Title: Prime numbers
Abstract: In my talk I will pose several questions about prime
numbers. We will see that on the one hand some of them allow an answer
with a proof of just a few lines, on the other hand, some of them lead
to deep questions and conjectures not yet understood. This seems to
represent a general pattern in mathematics: your curiosity leads to a
study of easy questions related with quite deep structures. I will
give many examples, suggestions and references for further study.
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Speaker: Frans Oort (University of Utrecht)
Time: December 13 (Thursday), 4 - 5:30 pm
Title: Abelian varieties over finite fields
Abstract: In 1948 André Weil proved that the Frobenius morphism on an
abelian variety over a finite field with q elements has eigenvalues
with all absolute values equal to the square root of q. This was the
first case of a long chain of beautiful conjectures and results.
In 1968 Honda and Tate proved that conversely such an algebraic
integer can be realized as an eigenvalue of the Frobenius of an
abelian variety over that finite field: a simple construction of an
algebraic integer with some easy properties proves the existence of a
complicated arithmetic-geometric object.
We sketch a modern proof of this deep theorem of Weil. We indicate
what is used in the proof by Honda and Tate, and (open problem) we ask
for a proof of this elegant result along lines of algebraic geometry,
not using complex uniformization.
Material exposed in this talk is classical and well-understood by now.
We give examples and we sketch some applications.
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