---
res:
  bibo_abstract:
  - Illusie has suggested that one should think of the classifying group of $M_X^{gp}$-torsors
    on a logarithmically smooth curve $X$ over a standard logarithmic point as a logarithmic
    analogue of the Picard group of $X$. This logarithmic Picard group arises naturally
    as a quotient of the algebraic Picard group by lifts of the chip firing relations
    of the associated dual graph. We connect this perspective to Baker and Norine's
    theory of ranks of divisors on a finite graph, and to Amini and Baker's metrized
    complexes of curves. Moreover, we propose a definition of a combinatorial rank
    for line bundles on $X$ and prove that an analogue of the Riemann-Roch formula
    holds for our combinatorial rank. Our proof proceeds by carefully describing the
    relationship between the logarithmic Picard group on a logarithmic curve and the
    Picard group of the associated metrized complex. This approach suggests a natural
    categorical framework for metrized complexes, namely the category of logarithmic
    curves.@eng
  bibo_authorlist:
  - foaf_Person:
      foaf_givenName: Tyler
      foaf_name: Foster, Tyler
      foaf_surname: Foster
  - foaf_Person:
      foaf_givenName: Dhruv
      foaf_name: Ranganathan, Dhruv
      foaf_surname: Ranganathan
  - foaf_Person:
      foaf_givenName: Mattia
      foaf_name: Talpo, Mattia
      foaf_surname: Talpo
  - foaf_Person:
      foaf_givenName: Martin
      foaf_name: Ulirsch, Martin
      foaf_surname: Ulirsch
      foaf_workInfoHomepage: http://www.librecat.org/personId=114697
  dct_date: 2016^xs_gYear
  dct_language: eng
  dct_title: Logarithmic Picard groups, chip firing, and the combinatorial rank@
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