Canonical extensions, irregularities, and the Swan conductor

AbstractUnder the local Langlands correspondence, the conductor of an irreducible representation of Gln(F) is greater than the Swan conductor of the corresponding Galois representation. In this paper, we establish the geometric analogue of this statement by showing that the conductor of a categorical representation of the loop group is greater than the irregularity of the corresponding meromorphic connection.

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Canonical extensions

Advanced Topics in Relation Algebras ◽

10.1007/978-3-319-65945-9_1 ◽

2017 ◽

pp. 1-100

Author(s):

Steven Givant

Keyword(s):

Canonical Extensions

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Canonical Extensions, Esakia Spaces, and Universal Models

Leo Esakia on Duality in Modal and Intuitionistic Logics - Outstanding Contributions to Logic ◽

10.1007/978-94-017-8860-1_2 ◽

2014 ◽

pp. 9-41 ◽

Cited By ~ 6

Author(s):

Mai Gehrke

Keyword(s):

Universal Models ◽

Canonical Extensions

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Canonical extensions and ultraproducts of polarities

Algebra Universalis ◽

10.1007/s00012-018-0562-4 ◽

2018 ◽

Vol 79 (4) ◽

Cited By ~ 2

Author(s):

Robert Goldblatt

Keyword(s):

Canonical Extensions

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Arithmetic 𝒟-modules on the unit disk. With an appendix by Shigeki Matsuda

Compositio Mathematica ◽

10.1112/s0010437x11005471 ◽

2011 ◽

Vol 148 (1) ◽

pp. 227-268 ◽

Cited By ~ 5

Author(s):

Richard Crew

Keyword(s):

Unit Disk ◽

Valuation Ring ◽

Discrete Valuation Ring ◽

Mixed Characteristic ◽

Complete Discrete Valuation Ring ◽

Canonical Extensions

AbstractLet 𝒱 be a complete discrete valuation ring of mixed characteristic. We classify arithmetic 𝒟-modules on Spf(𝒱[[t]]) up to certain kind of ‘analytic isomorphism’. This result is used to construct canonical extensions (in the sense of Katz and Gabber) for objects of this category.

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