A note on a theorem of Cadoret and Tamagawa

2018 ◽  
Vol 14 (02) ◽  
pp. 349-353
Author(s):  
Seyfi Türkelli
Keyword(s):  
Number Fields ◽  
Expander Graphs ◽  
Image Theorem

We prove Cadoret and Tamagawa’s open image theorem for curves defined over number fields using their arguments and the machinery of Ellenberg–Hall–Kowalski employed in their paper on expander graphs.

scholarly journals Cutting towers of number fields

2021 ◽  
Author(s):  
Farshid Hajir ◽  
Christian Maire ◽  
Ravi Ramakrishna
Keyword(s):  
Number Fields

scholarly journals Theta series and number fields: theorems and experiments

2021 ◽  
Author(s):  
Adrian Barquero-Sanchez ◽  
Guillermo Mantilla-Soler ◽  
Nathan C. Ryan
Keyword(s):  
Theta Series ◽  
Number Fields

Kummer theory for number fields via entanglement groups

2021 ◽  
Author(s):  
Antonella Perucca ◽  
Pietro Sgobba ◽  
Sebastiano Tronto
Keyword(s):  
Number Fields ◽  
Kummer Theory

scholarly journals Hyperbolic tessellations and generators of for imaginary quadratic fields

2021 ◽  
Vol 9 ◽  
Author(s):  
David Burns ◽  
Rob de Jeu ◽  
Herbert Gangl ◽  
Alexander D. Rahm ◽  
Dan Yasaki
Keyword(s):  
Number Field ◽  
Number Fields ◽  
Quadratic Fields ◽  
Quadratic Number ◽  
Imaginary Quadratic Fields ◽  
Quadratic Number Fields ◽  
Formula Group ◽  
Imaginary Quadratic Number ◽  
Direct Calculations

Abstract We develop methods for constructing explicit generators, modulo torsion, of the $K_3$ -groups of imaginary quadratic number fields. These methods are based on either tessellations of hyperbolic $3$ -space or on direct calculations in suitable pre-Bloch groups and lead to the very first proven examples of explicit generators, modulo torsion, of any infinite $K_3$ -group of a number field. As part of this approach, we make several improvements to the theory of Bloch groups for $ K_3 $ of any field, predict the precise power of $2$ that should occur in the Lichtenbaum conjecture at $ -1 $ and prove that this prediction is valid for all abelian number fields.

scholarly journals The 2-rank of the class group of some real cyclic quartic number fields

2021 ◽  
Vol 131 (1) ◽  
Author(s):  
Abdelmalek Azizi ◽  
Mohammed Tamimi ◽  
Abdelkader Zekhnini
Keyword(s):  
Class Group ◽  
Number Fields
Sign in / Sign up

Export Citation Format

Share Document