EISENSTEIN POLYNOMIALS DEFINING CYCLIC p-ADIC FIELDS WITH MINIMAL WILD RAMIFICATION

2021 ◽  
Vol 49 (1) ◽  
pp. 93-100
Author(s):  
Chad Awtrey ◽  
D. Haydn Stucker
Keyword(s):  
Wild Ramification

scholarly journals Wild ramification and a vanishing cycles formula

2004 ◽  
Vol 273 (1) ◽  
pp. 108-128 ◽  
Author(s):  
Mohamed Saı̈di
Keyword(s):  
Wild Ramification ◽  
Vanishing Cycles

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.

scholarly journals Wild ramification and restrictions to curves

2018 ◽  
Vol 29 (08) ◽  
pp. 1850052 ◽  
Author(s):  
Hiroki Kato
Keyword(s):  
Local Field ◽  
Arbitrary Dimension ◽  
Closed Field ◽  
Cohomology Groups ◽  
Algebraically Closed Field ◽  
Wild Ramification

We prove that wild ramification of a constructible sheaf on a surface is determined by that of the restrictions to all curves. We deduce from this result that the Euler–Poincaré characteristic of a constructible sheaf on a variety of arbitrary dimension over an algebraically closed field is determined by wild ramification of the restrictions to all curves. We similarly deduce from it that so is the alternating sum of the Swan conductors of the cohomology groups, for a constructible sheaf on a variety over a local field.

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