| Type of Document |
Dissertation |
| Author |
Johnson, Jennifer Michelle
|
| URN |
etd-06062005-134908 |
| Persistent URL |
http://resolver.caltech.edu/CaltechETD:etd-06062005-134908 |
| Title |
Artin L-functions for abelian extensions of imaginary quadratic fields |
| Degree |
PhD |
| Option |
Mathematics |
| Advisory Committee |
| Advisor Name |
Title |
| Matthias Flach |
Committee Chair |
| David G. Wales |
Committee Member |
| Dinakar Ramakrishnan |
Committee Member |
| Mladen Dimitrov |
Committee Member |
|
| Keywords |
- Euler system
- imaginary quadratic fields
- Tamagawa number conjecture
- L-functions
|
| Date of Defense |
2005-05-26 |
| Availability |
unrestricted |
Abstract
Let F be an abelian extension of an imaginary quadratic field K with Galois group G. We form the Galois-equivariant L-function of the motive h(Spec F)(j) where the Tate twists j are negative integers. The leading term in the Taylor expansion at s=0 decomposes over the group algebra Q[G] into a product of Artin L-functions indexed by the characters of G. We construct a motivic element via the Eisenstein symbol and relate the L-value to periods via regulator maps. Working toward the equivariant Tamagawa number conjecture, we prove that the L-value gives a basis in etale cohomology which coincides with the basis given by the p-adic L-function according to the main conjecture of Iwasawa theory.
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| Files |
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56K Modem |
ISDN (64 Kb) |
ISDN (128 Kb) |
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cv.pdf |
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thesis.pdf |
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