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Number Theory
Student Seminar
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to our next gathering
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Time: Place: |
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A Quick Introduction to Euler Systems
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Speaker: |
Kazim Buyukboduk (Stanford University)
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| Abstract: |
In this talk, I will aim to explain the basic ideas behind the Euler System Machinery. I will first define various Selmer groups and the applications of Poitou-Tate global duality, by means of bounding the dual Selmer group. At this point, it will be made explicit what Euler System machinery provides to bound the Selmer groups. I will then go ahead and give the definition of an Euler System, and exhibit the standard theorems provided by the Euler System argument. I certainly will omit almost all the details, however a number of examples will be presented. At the end, if time remains, I will shortly discuss the crucial properties of the so called Kolyvagin Systems, a sequence of cohomology classes derived from an Euler System, which essentially, together with global duality, give the bounds we seek. |
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