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Estimates for the Artin conductor

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Amalia Pizarro
Universidad de Valparaíso/MPIM
Wed, 2019-10-23 14:30 - 15:30
MPIM Lecture Hall
Parent event: 
Number theory lunch seminar

By using geometry of numbers, Minkowski showed that there exists a constant C such that if D_K is the discriminant of a number field K, then |D_K|>C^[K:Q]. In 1978, from the existence of  infinite class field towers, Martinet constructed  sequences of number fi elds of growing degree and  bounded root discriminant.

It is natural to ask if it is possible to extends the previous results to the Artin conductor.

In 1977 Odlyzko,  found the first nontrivial lower bounds for the conductor and in 2011, by using analytic methods, we improved these bounds. 

In this talk, we will review the previous results and in particular let us see the existence of irreducible Artin characters of growing degree with bounded root conductors.

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