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http://arks.princeton.edu/ark:/88435/dsp01x920g107d
Title: | Construction of an anticyclotomic Euler system with applications |
Authors: | Do, Kim Tuan |
Advisors: | Skinner, Christopher |
Contributors: | Mathematics Department |
Keywords: | Euler system Iwasawa theory |
Subjects: | Mathematics |
Issue Date: | 2022 |
Publisher: | Princeton, NJ : Princeton University |
Abstract: | In this thesis, we construct a new anticyclotomic Euler system (in the sense of Jetchev-Nekovar-Skinner (JNS)) for the Galois representation attached to a newform f of weight 2k twisted by an anticyclotomic Hecke character \chi of infinity type (l,−l), denoted by V_f(\chi), when the Heegner Hypothesis is not satisfied. The main ingredients for our construction are the Bertolini-Seveso-Venerucci (BSV) diagonal classes and the Lei-Loeffler-Zerbes norm maps. We then show some arithmetic applications of the constructed Euler system, including the rank 0 Bloch-Kato Conjecture for V_f(\chi) when k>=l+1, using the explicit reciprocity law of BSV and the machinery of JNS. |
URI: | http://arks.princeton.edu/ark:/88435/dsp01x920g107d |
Alternate format: | The Mudd Manuscript Library retains one bound copy of each dissertation. Search for these copies in the library's main catalog: catalog.princeton.edu |
Type of Material: | Academic dissertations (Ph.D.) |
Language: | en |
Appears in Collections: | Mathematics |
Files in This Item:
File | Description | Size | Format | |
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Do_princeton_0181D_14213.pdf | 724.08 kB | Adobe PDF | View/Download |
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