The p-adic monodromy-weight conjecture for p-adically uniformized varieties

Ehud De Shalit*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

11 Scopus citations

Abstract

A p-adically uniformized variety is a smooth projective variety whose associated rigid analytic space admits a uniformization by Drinfeld's p-adic symmetric domain. For such a variety we prove the monodromy-weight conjecture, which asserts that two independently defined filtrations on the log-crystalline cohomology of the special fiber in fact coincide. The proof proceeds by reducing the conjecture to a combinatorial statement about harmonic cochains on the Bruhat-Tits building, which was verified in our previous work.

Original languageAmerican English
Pages (from-to)101-120
Number of pages20
JournalCompositio Mathematica
Volume141
Issue number1
DOIs
StatePublished - Jan 2005

Keywords

  • Crystalline cohomology
  • Monodromy
  • p-adic uniformization

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