p -adic Abelian Stark conjectures at s = 1

David Solomon[1]

  • [1] King's College London, Department of Mathematics, Strand, London WC2R 2LS (Royaume-Uni)

Annales de l’institut Fourier (2002)

  • Volume: 52, Issue: 2, page 379-417
  • ISSN: 0373-0956

Abstract

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A p -adic version of Stark’s Conjecture at s = 1 is attributed to J.-P. Serre and stated (faultily) in Tate’s book on the Conjecture. Building instead on our previous paper (and work of Rubin) on the complex abelian case, we give a new approach to such a conjecture for real ray-class extensions of totally real number fields. We study the coherence of our p -adic conjecture and then formulate some integral refinements, both alone and in combination with its complex analogue. A ‘Weak Combined Refined’ version is discussed in more detail and proved in two special cases.

How to cite

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Solomon, David. "$p$-adic Abelian Stark conjectures at $s=1$." Annales de l’institut Fourier 52.2 (2002): 379-417. <http://eudml.org/doc/115984>.

@article{Solomon2002,
abstract = {A $p$-adic version of Stark’s Conjecture at $s=1$ is attributed to J.-P. Serre and stated (faultily) in Tate’s book on the Conjecture. Building instead on our previous paper (and work of Rubin) on the complex abelian case, we give a new approach to such a conjecture for real ray-class extensions of totally real number fields. We study the coherence of our $p$-adic conjecture and then formulate some integral refinements, both alone and in combination with its complex analogue. A ‘Weak Combined Refined’ version is discussed in more detail and proved in two special cases.},
affiliation = {King's College London, Department of Mathematics, Strand, London WC2R 2LS (Royaume-Uni)},
author = {Solomon, David},
journal = {Annales de l’institut Fourier},
keywords = {Stark conjecture; $p$-adic; L-function; zeta-function; abelian extension; unit; $S$-unit; regular; special value; totally real field; -adic -function; S-unit},
language = {eng},
number = {2},
pages = {379-417},
publisher = {Association des Annales de l'Institut Fourier},
title = {$p$-adic Abelian Stark conjectures at $s=1$},
url = {http://eudml.org/doc/115984},
volume = {52},
year = {2002},
}

TY - JOUR
AU - Solomon, David
TI - $p$-adic Abelian Stark conjectures at $s=1$
JO - Annales de l’institut Fourier
PY - 2002
PB - Association des Annales de l'Institut Fourier
VL - 52
IS - 2
SP - 379
EP - 417
AB - A $p$-adic version of Stark’s Conjecture at $s=1$ is attributed to J.-P. Serre and stated (faultily) in Tate’s book on the Conjecture. Building instead on our previous paper (and work of Rubin) on the complex abelian case, we give a new approach to such a conjecture for real ray-class extensions of totally real number fields. We study the coherence of our $p$-adic conjecture and then formulate some integral refinements, both alone and in combination with its complex analogue. A ‘Weak Combined Refined’ version is discussed in more detail and proved in two special cases.
LA - eng
KW - Stark conjecture; $p$-adic; L-function; zeta-function; abelian extension; unit; $S$-unit; regular; special value; totally real field; -adic -function; S-unit
UR - http://eudml.org/doc/115984
ER -

References

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