On p-adic abelian Stark Conjectures at s=1

TY - JOUR

T1 - On p-adic abelian Stark Conjectures at s=1

AU - Solomon, D

PY - 2002

Y1 - 2002

N2 - 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.

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.

UR - https://www.scopus.com/pages/publications/0037828379

M3 - Article

VL - 52

SP - 379

EP - 417

JO - ANNALES- INSTITUT FOURIER

JF - ANNALES- INSTITUT FOURIER

IS - 2

ER -