scholarly journals Generalized Monodromy Conjecture in dimension two

2012 ◽  
Vol 16 (1) ◽  
pp. 155-217 ◽  
Author(s):  
András Némethi ◽  
Willem Veys
Keyword(s):  
Monodromy Conjecture

scholarly journals The monodromy conjecture for a space monomial curve with a plane semigroup

2021 ◽  
Vol 65 ◽  
pp. 529-597
Author(s):  
Jorge Martín-Morales ◽  
Willem Veys ◽  
Lena Vos
Keyword(s):  
Monodromy Conjecture ◽  
Monomial Curve

scholarly journals Degeneration of Kummer surfaces

2020 ◽  
pp. 1-33
Author(s):  
OTTO OVERKAMP
Keyword(s):  
Galois Representation ◽  
Base Change ◽  
Abelian Surface ◽  
Kummer Surface ◽  
Semistable Reduction ◽  
Valued Field ◽  
Monodromy Conjecture ◽  
Finite Base ◽  
Kummer Surfaces ◽  
Special Fibre

Abstract We prove that a Kummer surface defined over a complete strictly Henselian discretely valued field K of residue characteristic different from 2 admits a strict Kulikov model after finite base change. The Kulikov models we construct will be schemes, so our results imply that the semistable reduction conjecture is true for Kummer surfaces in this setup, even in the category of schemes. Our construction of Kulikov models is closely related to an earlier construction of Künnemann, which produces semistable models of Abelian varieties. It is well known that the special fibre of a strict Kulikov model belongs to one of three types, and we shall prove that the type of the special fibre of a strict Kulikov model of a Kummer surface and the toric rank of a corresponding Abelian surface are determined by each other. We also study the relationship between this invariant and the Galois representation on the second ℓ-adic cohomology of the Kummer surface. Finally, we apply our results, together with earlier work of Halle–Nicaise, to give a proof of the monodromy conjecture for Kummer surfaces in equal characteristic zero.

scholarly journals The Monodromy Conjecture for hyperplane arrangements

2011 ◽  
Vol 153 (1) ◽  
pp. 131-137 ◽  
Author(s):  
Nero Budur ◽  
Mircea Mustaţă ◽  
Zach Teitler
Keyword(s):  
Hyperplane Arrangements ◽  
Monodromy Conjecture

On local monodromy filtrations attached to motives

2017 ◽  
Vol 13 (03) ◽  
pp. 801-817 ◽  
Author(s):  
Abhijit Laskar
Keyword(s):  
Number Fields ◽  
Local Weight ◽  
Monodromy Conjecture ◽  
Special Cases ◽  
Local Monodromy

We prove special cases, of an analogue of the (local) weight monodromy conjecture, for motives over number fields. This enables us to show in many new cases that the local [Formula: see text]-factors of these motives are well defined, i.e. depend only on the motive and the valuations, and not on the chosen prime [Formula: see text] for the [Formula: see text]-adic realization.

scholarly journals Monodromy conjecture for some surface singularities

2002 ◽  
Vol 35 (4) ◽  
pp. 605-640 ◽  
Author(s):  
E ARTALBARTOLO ◽  
P CASSOUNOGUES ◽  
I LUENGO ◽  
A MELLEHERNANDEZ
Keyword(s):  
Monodromy Conjecture ◽  
Surface Singularities
Sign in / Sign up

Export Citation Format

Share Document