O hypotéze týkající se minus částí ve stylu Grosse

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14310%2F08%3A00025891" target="_blank" >RIV/00216224:14310/08:00025891 - isvavai.cz</a>

Výsledek na webu

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DOI - Digital Object Identifier

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Jazyk výsledku

angličtina

Název v původním jazyce

On a conjecture concerning minus parts in the style of Gross

Popis výsledku v původním jazyce

This paper is devoted to Gross's conjecture on tori over the base field Q. We call it the Minus Conjecture, since it involves a regulator built from units in the minus part. We recall and develop its relation to a conjecture of Burns, which is now knownto hold generally in the absolutely abelian setting; however in many situations it is not clear at all how one should deduce the Minus Conjecture from it. We prove a somewhat weaker statement (order of vanishing) rather generally, and we give a proof ofthe Minus Conjecture for some specific classes of absolutely abelian extensions K/Q, for which K^+/Q is l-elementary and ramified in at most two primes. The field K is assumed to be of the form FK^+ where F is an arbitrary imaginary quadratic field. Ourmethods involve a good deal of explicit calculation; among other things, we use p-adic Gamma-functions and the Gross-Koblitz formula.

Název v anglickém jazyce

On a conjecture concerning minus parts in the style of Gross

Popis výsledku anglicky

This paper is devoted to Gross's conjecture on tori over the base field Q. We call it the Minus Conjecture, since it involves a regulator built from units in the minus part. We recall and develop its relation to a conjecture of Burns, which is now knownto hold generally in the absolutely abelian setting; however in many situations it is not clear at all how one should deduce the Minus Conjecture from it. We prove a somewhat weaker statement (order of vanishing) rather generally, and we give a proof ofthe Minus Conjecture for some specific classes of absolutely abelian extensions K/Q, for which K^+/Q is l-elementary and ramified in at most two primes. The field K is assumed to be of the form FK^+ where F is an arbitrary imaginary quadratic field. Ourmethods involve a good deal of explicit calculation; among other things, we use p-adic Gamma-functions and the Gross-Koblitz formula.

Druh

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

CEP obor

BA - Obecná matematika

OECD FORD obor

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Projekt

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Návaznosti

Z - Vyzkumny zamer (s odkazem do CEZ)

Rok uplatnění

2008

Kód důvěrnosti údajů

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

Název periodika

Acta Arithmetica

ISSN

0065-1036

e-ISSN

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Svazek periodika

132

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

PL - Polská republika

Počet stran výsledku

48

Strana od-do

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Kód UT WoS článku

000258702800001

EID výsledku v databázi Scopus

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