Integral and 𝑝-adic refinements of the abelian Stark conjecture

The Rubin?Stark Conjecture for imaginary abelian fields of odd prime power conductor

Mathematische Annalen ◽

10.1007/s00208-004-0546-x ◽

2004 ◽

Vol 330 (2) ◽

Cited By ~ 2

Author(s):

Cristian D. Popescu

Keyword(s):

Prime Power ◽

Abelian Fields ◽

Stark Conjecture

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On the elliptic Stark conjecture at primes of multiplicative reduction

Indiana University Mathematics Journal ◽

10.1512/iumj.2019.68.7704 ◽

2019 ◽

Vol 68 (4) ◽

pp. 1233-1253

Author(s):

Daniele Casazza ◽

Victor Rotger

Keyword(s):

Stark Conjecture

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On the Gross–Stark Conjecture

Annals of Mathematics ◽

10.4007/annals.2018.188.3.3 ◽

2018 ◽

Vol 188 (3) ◽

pp. 833 ◽

Cited By ~ 2

Author(s):

Samit Dasgupta ◽

Mahesh Kakde ◽

Kevin Ventullo

Keyword(s):

Stark Conjecture

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Fitting Ideals in Number Theory and Arithmetic

Jahresbericht der Deutschen Mathematiker-Vereinigung ◽

10.1365/s13291-021-00233-5 ◽

2021 ◽

Author(s):

Cornelius Greither

Keyword(s):

Number Theory ◽

Galois Group ◽

Classical Result ◽

Number Fields ◽

Class Groups ◽

Stark Conjecture

AbstractWe describe classical and recent results concerning the structure of class groups of number fields as modules over the Galois group. When presenting more modern developments, we can only hint at the much broader context and the very powerful general techniques that are involved, but we endeavour to give complete statements or at least examples where feasible. The timeline goes from a classical result proved in 1890 (Stickelberger’s Theorem) to a recent (2020) breakthrough: the proof of the Brumer-Stark conjecture by Dasgupta and Kakde.

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On the non-abelian Brumer–Stark conjecture and the equivariant Iwasawa main conjecture

Mathematische Zeitschrift ◽

10.1007/s00209-018-2152-8 ◽

2018 ◽

Vol 292 (3-4) ◽

pp. 1233-1267

Author(s):

Henri Johnston ◽

Andreas Nickel

Keyword(s):

Main Conjecture ◽

Stark Conjecture

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p-Adic measures associated with zeta values and p-adic log multiple gamma functions

International Journal of Number Theory ◽

10.1142/s1793042119500532 ◽

2019 ◽

Vol 15 (05) ◽

pp. 991-1007

Author(s):

Tomokazu Kashio

Keyword(s):

Number Fields ◽

Abelian Extension ◽

Gamma Functions ◽

Rank One ◽

Zeta Values ◽

Stark Conjecture ◽

Explicit Relation ◽

Text Unit

We study a relation between two refinements of the rank one abelian Gross–Stark conjecture. For a suitable abelian extension [Formula: see text] of number fields, a Gross–Stark unit is defined as a [Formula: see text]-unit of [Formula: see text] satisfying certain properties. Let [Formula: see text]. Yoshida and the author constructed the symbol [Formula: see text] by using [Formula: see text]-adic [Formula: see text] multiple gamma functions, and conjectured that the [Formula: see text] of a Gross–Stark unit can be expressed by [Formula: see text]. Dasgupta constructed the symbol [Formula: see text] by using the [Formula: see text]-adic multiplicative integration, and conjectured that a Gross–Stark unit can be expressed by [Formula: see text]. In this paper, we give an explicit relation between [Formula: see text] and [Formula: see text] and prove that two refinements are consistent.

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