For more information about this meeting, contact Robert Vaughan.
| Title: | Small Height and Infinite Non-abelian Extensions |
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| Seminar: | Algebra and Number Theory Seminar |
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| Speaker: | Philipp Habegger, IAS, Princeton |
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| Abstract: |
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| The absolute, logarithmic Weil height is non-negative and vanishes precisely at 0 and at the roots of unity. Moreover, when restricted to a number field there are no arbitrarily small, positive heights. Amoroso, Bombieri, David, Dvornicich, Schinzel, Zannier and others exhibited many infinite extensions of the rationals with a height gap. For example, the maximal abelian extension of any number field has this property. To see a non-abelian example, let E be an elliptic curve defined over the rationals without complex multiplication. The field K generated by all complex points of E with finite order is an infinite extension of the rationals. Its Galois group contains no commutative subgroup of finite index. In the talk, I will sketch a proof that K contains no elements of sufficiently small, positive height. |
Room Reservation Information
| Room Number: | MB106 |
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| Date: | 04 / 04 / 2013 |
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| Time: | 11:15am - 12:05pm |
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