Relative Bogomolov extensions

• Autorzy: Robert Grizzard
• Języki publikacji: EN

Abstrakty

EN

A subfield K ⊆ ℚ̅ has the Bogomolov property if there exists a positive ε such that no non-torsion point of $K^{×}$ has absolute logarithmic height below ε. We define a relative extension L/K to be Bogomolov if this holds for points of $L^{×}∖K^{×}$. We construct various examples of extensions which are and are not Bogomolov. We prove a ramification criterion for this property, and use it to show that such extensions can always be constructed if some rational prime has bounded ramification index in K.

Kategorie tematyczne

• 12F05: Algebraic extensions
• 11G50: Heights
• 11R21: Other number fields
• 11R04: Algebraic numbers; rings of algebraic integers
• 11S05: Polynomials

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 2015
• Tom: 170
• Numer: 1
• Strony: 1-13

Daty

wydano

2015

Twórcy

autor

Robert Grizzard

• Department of Mathematics, University of Wisconsin-Madison, 480 Lincoln Dr., Madison, WI 53706-1325, U.S.A.

Identyfikatory

DOI

10.4064/aa170-1-1