Comparison theorem between Fourier transform and Fourier transform with compact support

Huyghe, Christine

doi:10.5802/jtnb.827

Cited by 2 publications

(2 citation statements)

References 3 publications

(4 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…is well-defined, and also showed an analog of the result of Katz and Laumon [60,Theorem 3.2]. Namely, the canonical homomorphism…”

Section: Geometric Fourier Transformsmentioning

confidence: 57%

Product formula forp-adic epsilon factors

Abe¹,

Marmora²

2014

J. Inst. Math. Jussieu

View full text Add to dashboard Cite

Let X be a smooth proper curve over a finite field of characteristic p. We prove a product formula for p-adic epsilon factors of arithmetic D-modules on X. In particular we deduce the analogous formula for overconvergent F -isocrystals, which was conjectured previously. The p-adic product formula is the equivalent in rigid cohomology of the Deligne-Laumon formula for epsilon factors in ℓ-adicétale cohomology (for ℓ = p). One of the main tools in the proof of this p-adic formula is a theorem of regular stationary phase for arithmetic D-modules that we prove by microlocal techniques.

show abstract

“…is well-defined, and also showed an analog of the result of Katz and Laumon [60,Theorem 3.2]. Namely, the canonical homomorphism…”

Section: Geometric Fourier Transformsmentioning

confidence: 57%

Product formula forp-adic epsilon factors

Abe¹,

Marmora²

2014

J. Inst. Math. Jussieu

View full text Add to dashboard Cite

show abstract

“…The purpose of this subsection is recalling the theory of Fourier transforms of arithmetic D-modules, which is closely related to the theory of multiplicative convolution. The basic references are articles of Huyghe [NH1,NH2]. Her theory of p-adic Fourier transforms is the one with respect to the character ψ which can be expressed by ψ 0 •Tr k/k 0 (in other words, for which π ψ is a root of X p−1 + p).…”

Section: Fourier Transformmentioning

confidence: 99%

p-adic Generalized Hypergeometric Equations from the Viewpoint of Arithmetic D-modules

Miyatani

2016

Preprint

View full text Add to dashboard Cite

We study the p-adic (generalized) hypergeometric equations by using the theory of multiplicative convolution of arithmetic D-modules. As a result, we prove that the hypergeometric isocrystals with suitable rational parameters have a structure of overconvergent F -isocrystals. 0 Introduction. Katz [Ka, 5.3.1] discovered that the hypergeometric D-modules on A 1 C \{0} can be described as the multiplicative convolution of hypergeometric D-modules of rank one. Precisely speaking, Katz proved the statement (ii) in the following theorem (the statement (i) is trivial but put to compare with another theorem later).Convolution Theorem over C. Let α = (α 1 , . . . , α m ) and β = (β 1 , . . . , β n ) be two sequences of complex numbers and assume that α i −β j is not an integer for any i , j . Let Hyp(α;β) be the D-module on G m,C defined by the hypergeometric operatorThen, Hyp π (α; β) has the following properties.(i) If m = n, then Hyp π (α; β) has a structure of an overconvergent F -isocrystal on G m,k of rank max {m, n}. If m = n, then the restriction of Hyp π (α; β) to P 1 V \{0, 1, ∞} has a structure of an overconvergent F -isocrystal on G m,k \{1} of rank m.

show abstract

Comparison theorem between Fourier transform and Fourier transform with compact support

Cited by 2 publications

References 3 publications

Product formula forp-adic epsilon factors

Product formula forp-adic epsilon factors

p-adic Generalized Hypergeometric Equations from the Viewpoint of Arithmetic D-modules

Contact Info

Product

Resources

About