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Random Galois extensions of Hilbertian fields
Random Galois extensions Hilbertian fields Number Theory
2012/6/21
Let L be a Galois extension of a countable Hilbertian field K. Although L need not be Hilbertian, we prove that an abundance of large Galois subextensions of L/K are.
On Zagier's conjecture for base extensions of elliptic curves
Zagier's conjecture base extensions of elliptic curves Number Theory
2012/4/18
Let E be an elliptic curve over Q, and let F be a finite abelian extension of Q. Using Beilinson's theorem on a suitable modular curve, we prove a weak version of Zagier's conjecture for L(E/F,2), whe...
The intersection of cyclic Kummer extensions with cyclotomic extensions
cyclic Kummer extensions cyclotomic extensions Number Theory
2011/9/19
Abstract: We study to which extent cyclic Kummer extensions can be contained in a cyclotomic extension. Let K be a field, and consider an extension of K of the form K(z_m, sqrt[n]{a}) where a is in K,...
Distribution of Artin-Schreier extensions
Artin-Schreier extensions Number Theory noncyclic elementary abelian extensions
2011/8/25
Abstract: The article at hand contains exact asymptotic formulas for the distribution of conductors of elementary abelian p-extensions of global function fields of characteristic p. As a consequence f...
On logarithmic extensions of local scale-invariance
logarithmic extensions local scale-invariance
2010/12/16
The known logarithmic extensions of conformal and Schr¨odinger-invariance assume translation-invariance in their spatial and temporal coordinates. Therefore, they cannot be applied directly to slow fa...
Field Extensions Having the Unique Subfield Property, and G-Cogalois Extensions
Field extension separable extension simple extension radical extension G--Cogalois extension unique subfield property classical Kummer extension
2010/3/1
We present a short proof, based on Cogalois Theory, of a result due to Acosta de Orozco and Vélez (1982, J. Number Theory 15, 388-405) characterizing separable simple radical field extensions with the...