Guignard establishes a higher-dimensional factorization of global ε-factors into local contributions via iterated vanishing cycles and refined Artin conductors.
Deligne, ``Les constantes des \'equations fonctionnelles des fonctions L '', in ``Modular Functions of One Variable II'', Lecture Notes in Mathematics 349, Springer-Verlag, 1973
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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.