scholarly journals Wild Ramification in the Imperfect Residue Field Case

2018 ◽  
Author(s):  
Osamu Hyodo
Keyword(s):  
Residue Field ◽  
Field Case ◽  
Wild Ramification

scholarly journals Wild ramification and the characteristic cycle of an ℓ-adic sheaf

2009 ◽  
Vol 8 (4) ◽  
pp. 769-829 ◽  
Author(s):  
Takeshi Saito
Keyword(s):  
Local Field ◽  
Cotangent Bundle ◽  
Euler Number ◽  
Residue Field ◽  
Geometric Method ◽  
Characteristic Class ◽  
Wild Ramification ◽  
Characteristic Cycle

AbstractWe propose a geometric method to measure the wild ramification of a smooth étale sheaf along the boundary. Using the method, we study the graded quotients of the logarithmic ramification groups of a local field of characteristic p > 0 with arbitrary residue field. We also define the characteristic cycle of an ℓ-adic sheaf, satisfying certain conditions, as a cycle on the logarithmic cotangent bundle and prove that the intersection with the 0-section computes the characteristic class, and hence the Euler number.

Conductors in the Non-Separable Residue Field Case

1993 ◽  
pp. 1-34 ◽  
Author(s):  
Robert Boltje ◽  
G.-Martin Cram ◽  
V. P. Snaith
Keyword(s):  
Residue Field ◽  
Field Case

scholarly journals Faltings extension and Hodge-Tate filtration for abelian varieties over p-adic local fields with imperfect residue fields

2020 ◽  
pp. 1-17
Author(s):  
Tongmu He
Keyword(s):  
Abelian Varieties ◽  
Residue Field ◽  
Local Fields ◽  
Field Case ◽  
Residue Fields ◽  
Valuation Field

Abstract Let K be a complete discrete valuation field of characteristic $0$ , with not necessarily perfect residue field of characteristic $p>0$ . We define a Faltings extension of $\mathcal {O}_K$ over $\mathbb {Z}_p$ , and we construct a Hodge-Tate filtration for abelian varieties over K by generalizing Fontaine’s construction [Fon82] where he treated the perfect residue field case.

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