A Chebotarev density theorem for families of fields, with applications to class groups
Recent developments in Analytic Number Theory May 01, 2017 - May 05, 2017
Location: SLMath: Eisenbud Auditorium
Class groups
number fields
p-torsion
Chebotarev density theorem
Artin conjectures
11S82 - Non-Archimedean dynamical systems [See mainly 37Pxx]
11T30 - Structure theory for finite fields and commutative rings (number-theoretic aspects)
Pierce
This talk will present a new effective Chebotarev theorem that holds for all but a possible zero-density subfamily of certain families of number fields of fixed degree. For certain families, this work is unconditional, and in other cases it is conditional on the strong Artin conjecture and certain conjectures on counting number fields. As a result, we obtain nontrivial average upper bounds on p-torsion in the class groups of the families of fields.
Pierce.Notes
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Pierce
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