The Minus Conjecture revisited

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14310%2F09%3A00036301" target="_blank" >RIV/00216224:14310/09:00036301 - isvavai.cz</a>

Výsledek na webu

—

DOI - Digital Object Identifier

—

Jazyk výsledku

angličtina

Název v původním jazyce

The Minus Conjecture revisited

Popis výsledku v původním jazyce

In an earlier paper we proved some results concerning Gross's conjecture on tori. This conjecture, which we call the Minus Conjecture, is closely related to a conjecture of Burns, which is now known to hold generally in the absolutely abelian setting; however Burns' conjecture does not directly imply the Minus Conjecture. The result proved in the earlier paper was concerned with imaginary absolutely abelian extensions <i>K</i>/<b>Q</b> of the form <i>K</i>=<i>FK</i>⁺, with <i>F</i> imaginaryquadratic and <i>K</i>⁺/<b>Q</b> being tame, <i>l</i>-elementary and ramified at most at two primes. In the present paper we complement these results by proving the Minus Conjecture for extensions <i>K</i>/<b>Q</b> as above but without any restriction on the number s of ramified primes. The price we have to pay for this generality is that our proof only works if the odd prime <i>l</i>&gt;=3(<i>s</i>+1) and <i>l</i> does not divide <i>h_F</i>.

Název v anglickém jazyce

The Minus Conjecture revisited

Popis výsledku anglicky

In an earlier paper we proved some results concerning Gross's conjecture on tori. This conjecture, which we call the Minus Conjecture, is closely related to a conjecture of Burns, which is now known to hold generally in the absolutely abelian setting; however Burns' conjecture does not directly imply the Minus Conjecture. The result proved in the earlier paper was concerned with imaginary absolutely abelian extensions <i>K</i>/<b>Q</b> of the form <i>K</i>=<i>FK</i>⁺, with <i>F</i> imaginaryquadratic and <i>K</i>⁺/<b>Q</b> being tame, <i>l</i>-elementary and ramified at most at two primes. In the present paper we complement these results by proving the Minus Conjecture for extensions <i>K</i>/<b>Q</b> as above but without any restriction on the number s of ramified primes. The price we have to pay for this generality is that our proof only works if the odd prime <i>l</i>&gt;=3(<i>s</i>+1) and <i>l</i> does not divide <i>h_F</i>.

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

BA - Obecná matematika

OECD FORD obor

—

Projekt

—

Návaznosti

Z - Vyzkumny zamer (s odkazem do CEZ)<br>S - Specificky vyzkum na vysokych skolach

Rok uplatnění

2009

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Journal für die reine und angewandte Mathematik

ISSN

0075-4102

e-ISSN

—

Svazek periodika

632

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

DE - Spolková republika Německo

Počet stran výsledku

16

Strana od-do

—

Kód UT WoS článku

000269065800006

EID výsledku v databázi Scopus

—