Class Field Theory, D-Modules, and Ramification on Higher Dimensional Schemes, Part I

DOI10.2307/2375001zbMath0864.11057OpenAlexW2322884426MaRDI QIDQ4306389

Kazuya Kato

Publication date: 22 June 1997

Published in: American Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2307/2375001

zbMATH Keywords

characteristic cycle\({\mathcal D}\)-moduleclass field theorySwan conductorSerre's conjectureArtin characters for higher dimensional regular local ringsinvariants of wild ramificationramification in finite coverings of higher dimensional schemesramification of Galois representationsRiemann-Roch formula for \(\ell\)-adic sheaves of rank one

Mathematics Subject Classification ID

Riemann-Roch theorems (14C40) Geometric class field theory (11G45) Differentials and other special sheaves; D-modules; Bernstein-Sato ideals and polynomials (14F10) Class field theory (11R37) Generalized class field theory ((K)-theoretic aspects) (19F05)

Related Items (21)

RECIPROCITY SHEAVES AND THEIR RAMIFICATION FILTRATIONS ⋮ Good formal structures for flat meromorphic connections. III: Irregularity and turning loci ⋮ Ramification theory for Artin-Schreier extensions of valuation rings ⋮ A torsion formula for the epsilon factor of a character on a surface ⋮ Ramification theory for degree \(p\) extensions of arbitrary valuation rings in mixed characteristic \((0,p)\) ⋮ Wild ramification and the characteristic cycle of an ℓ-adic sheaf ⋮ Ramification theory for varieties over a local field ⋮ Equality of two non-logarithmic ramification filtrations of abelianized Galois group in positive characteristic ⋮ The characteristic class and ramification of an \(\ell\)-adic étale sheaf ⋮ Characteristic cycle of a rank one sheaf and ramification theory ⋮ On localizations of the characteristic classes of \(\ell \)-adic sheaves and conductor formula in characteristic \(p > 0\) ⋮ Wild ramification and the cotangent bundle ⋮ On ramifications of Artin-Schreier extensions of surfaces over algebraically closed fields of positive characteristic. II. ⋮ Integration on valuation fields over local fields ⋮ Swan conductors for p-adic differential modules. II Global variation ⋮ Formule du conducteur pour un caractère l-adique ⋮ Ramification and cleanliness ⋮ Ramification of higher local fields, approaches and questions ⋮ On ramifications of Artin-Schreier extensions of surfaces over algebraically closed fields of positive characteristic I ⋮ Cleanliness and log-characteristic cycles for vector bundles with flat connections ⋮ From Pierre Deligne's secret garden: looking back at some of his letters

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