Guignard establishes a higher-dimensional factorization of global ε-factors into local contributions via iterated vanishing cycles and refined Artin conductors.
Contou-Carr\`ere, Jacobienne locale d'une courbe formelle relative, Rendiconti del Seminario Matematico della Universit\`a di Padova 130 (2013), pp.1-106
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Geometric local $\varepsilon$-factors in higher dimensions
Guignard establishes a higher-dimensional factorization of global ε-factors into local contributions via iterated vanishing cycles and refined Artin conductors.