Good elements and metric invariants in BdR +

Victor Alexandru, Nicolae Popescu, Alexandru Zaharescu

Research output: Contribution to journalArticle

Abstract

Let p be a prime, ℚp the field of p-adic numbers and ℚ̄p a fixed algebraic closure of ℚp. B dR + is the ring of p-adic periods of algebraic varieties over p-adic fields introduced by Fontaine. For each n one defines a canonical valuation wn on ℚ̄p such that B dR +n/In becomes the completion of ℚ̄p with respect to wn, where I is the maximal ideal of BdR +. An element α ∈ ℚ̄ p* is said to be good at level n if wn(α) = v(αa) where v denotes the p-adic valuation on ℚ̄p. The set script G signn of good elements at level n is a subgroup of ℚ̄p*. We prove that each quotient group ℚ̄p*/script G signn is a torsion group and that each quotient script G sign1/script G signn is a p-group. We also show that a certain sequence of metric invariants {l n(Z)}n∈ℕ associated to an element Z ∈ BdR +, is constant.

Original languageEnglish (US)
Pages (from-to)125-137
Number of pages13
JournalKyoto Journal of Mathematics
Volume43
Issue number1
DOIs
StatePublished - Dec 2003

ASJC Scopus subject areas

  • Mathematics(all)

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