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2008 Mass formulas for local Galois representations to wreath products and cross products
Melanie Wood
Algebra Number Theory 2(4): 391-405 (2008). DOI: 10.2140/ant.2008.2.391

Abstract

Bhargava proved a formula for counting, with certain weights, degree n étale extensions of a local field, or equivalently, local Galois representations to Sn. This formula is motivation for his conjectures about the density of discriminants of Sn-number fields. We prove there are analogous “mass formulas” that count local Galois representations to any group that can be formed from symmetric groups by wreath products and cross products, corresponding to counting towers and direct sums of étale extensions. We obtain as a corollary that the above mentioned groups have rational character tables. Our result implies that D4 has a mass formula for certain weights, but we show that D4 does not have a mass formula when the local Galois representations to D4 are weighted in the same way as representations to S4 are weighted in Bhargava’s mass formula.

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Melanie Wood. "Mass formulas for local Galois representations to wreath products and cross products." Algebra Number Theory 2 (4) 391 - 405, 2008. https://doi.org/10.2140/ant.2008.2.391

Information

Received: 28 November 2007; Revised: 31 March 2008; Accepted: 28 April 2008; Published: 2008
First available in Project Euclid: 20 December 2017

zbMATH: 1176.11063
MathSciNet: MR2411405
Digital Object Identifier: 10.2140/ant.2008.2.391

Subjects:
Primary: 11S15
Secondary: 11R45

Keywords: Counting Field Extension , Local Field , mass formula

Rights: Copyright © 2008 Mathematical Sciences Publishers

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Vol.2 • No. 4 • 2008
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