scholarly journals Integration of functions of motivic exponential class, uniform in all non-archimedean local fields of characteristic zero

2018 ◽  
Vol 5 ◽  
pp. 45-78 ◽  
Author(s):  
Raf Cluckers ◽  
Immanuel Halupczok
Keyword(s):  
Characteristic Zero ◽  
Local Fields

scholarly journals Meromorphic continuation of Koba-Nielsen string amplitudes

2020 ◽  
Vol 2020 (9) ◽  
Author(s):  
M. Bocardo-Gaspar ◽  
Willem Veys ◽  
W. A. Zúñiga-Galindo
Keyword(s):  
Characteristic Zero ◽  
Zeta Functions ◽  
Open String ◽  
Local Fields ◽  
Meromorphic Continuation ◽  
Partition Functions ◽  
Interesting Connection ◽  
Bona Fide ◽  
Local Zeta Functions ◽  
String Amplitudes

Abstract In this article, we establish in a rigorous mathematical way that Koba-Nielsen amplitudes defined on any local field of characteristic zero are bona fide integrals that admit meromorphic continuations in the kinematic parameters. Our approach allows us to study in a uniform way open and closed Koba-Nielsen amplitudes over arbitrary local fields of characteristic zero. In the regularization process we use techniques of local zeta functions and embedded resolution of singularities. As an application we present the regularization of p-adic open string amplitudes with Chan-Paton factors and constant B-field. Finally, all the local zeta functions studied here are partition functions of certain 1D log-Coulomb gases, which shows an interesting connection between Koba-Nielsen amplitudes and statistical mechanics.

scholarly journals Selberg integral over local fields

2019 ◽  
Vol 31 (5) ◽  
pp. 1085-1095
Author(s):  
Zenan Fu ◽  
Yongchang Zhu
Keyword(s):  
Characteristic Zero ◽  
Integral Formula ◽  
Local Fields ◽  
Selberg Integral

AbstractWe prove a version of the Selberg integral formula for local fields of characteristic zero.

Local Fields

1986 ◽  
Author(s):  
J. W. S. Cassels
Keyword(s):  
Local Fields

scholarly journals On the Voevodsky motive of the moduli space of Higgs bundles on a curve

2021 ◽  
Vol 27 (1) ◽  
Author(s):  
Victoria Hoskins ◽  
Simon Pepin Lehalleur
Keyword(s):  
Moduli Space ◽  
Moduli Spaces ◽  
Characteristic Zero ◽  
Rational Point ◽  
Triangulated Category ◽  
Higgs Bundles ◽  
Projective Curve ◽  
Smooth Projective Curve ◽  
De Rham

AbstractWe study the motive of the moduli space of semistable Higgs bundles of coprime rank and degree on a smooth projective curve C over a field k under the assumption that C has a rational point. We show this motive is contained in the thick tensor subcategory of Voevodsky’s triangulated category of motives with rational coefficients generated by the motive of C. Moreover, over a field of characteristic zero, we prove a motivic non-abelian Hodge correspondence: the integral motives of the Higgs and de Rham moduli spaces are isomorphic.

scholarly journals Conjectures on Stably Newton Degenerate Singularities

2021 ◽  
Author(s):  
Jan Stevens
Keyword(s):  
Characteristic Zero ◽  
Arbitrary Number ◽  
Milnor Number ◽  
Plane Curves ◽  
Newton Diagram ◽  
Finite Characteristic ◽  
Vanishing Cycles

AbstractWe discuss a problem of Arnold, whether every function is stably equivalent to one which is non-degenerate for its Newton diagram. We argue that the answer is negative. We describe a method to make functions non-degenerate after stabilisation and give examples of singularities where this method does not work. We conjecture that they are in fact stably degenerate, that is not stably equivalent to non-degenerate functions.We review the various non-degeneracy concepts in the literature. For finite characteristic, we conjecture that there are no wild vanishing cycles for non-degenerate singularities. This implies that the simplest example of singularities with finite Milnor number, $$x^p+x^q$$ x p + x q in characteristic p, is not stably equivalent to a non-degenerate function. We argue that irreducible plane curves with an arbitrary number of Puiseux pairs (in characteristic zero) are stably non-degenerate. As the stabilisation involves many variables, it becomes very difficult to determine the Newton diagram in general, but the form of the equations indicates that the defining functions are non-degenerate.

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