18 citations · 62 across the 17 of their papers we have counts for
14 papers · 1 filter
A comparison between compactly supported rigid and -module cohomology
Tomoyuki Abe, Christopher Lazda
The goal of this article is to prove a comparison theorem between rigid cohomology and cohomology computed using the theory of arithmetic -modules. To do this, we cons…
Ramification theory from homotopical point of view, II
Tomoyuki Abe
This is the second part of the paper which proves the compatibility of pushforward along a proper morphism of an étale constructible sheaf and the pushforward of its characteristic…
Ramification theory from homotopical point of view, I
Tomoyuki Abe
We prove the compatibility of pushforward along a proper morphism of an étale constructible sheaf and the pushforward of its characteristic cycle up to -torsion. This was conjec…
Trace formalism for motivic cohomology
Tomoyuki Abe
The goal of this paper is to construct trace maps for the six functor formalism of motivic cohomology after Voevodsky, Ayoub, and Cisinski-Déglise. We also construct an -en…
Proper pushforwards on analytic adic spaces
Tomoyuki Abe, Christopher Lazda
We construct proper pushforwards for partially proper morphisms of analytic adic spaces. This generalises the theory due to van der Put in the case of rigid analytic varieties over…
Around the nearby cycle functor for arithmetic -modules
Tomoyuki Abe
We will establish a nearby and vanishing cycle formalism for the arithmetic -module theory following Beilinson's philosophy. As an application, we define smooth object…
A Lefschetz theorem for overconvergent isocrystals with Frobenius structure
Tomoyuki Abe, Hélène Esnault
We show a Lefschetz theorem for irreducible overconvergent -isocrystals on smooth varieties defined over a finite field. We derive several consequences from it.
Langlands correspondence for isocrystals and the existence of crystalline companions for curves
Tomoyuki Abe
In this paper, we show the Langlands correspondence for isocrystals on curves. This shows the existence of crystalline companion in the curve case. For the proof, we construct the…
On Beilinson's equivalence for -adic cohomology
Tomoyuki Abe, Daniel Caro
In this short note, we show a p-adic analogue of Beilinson's equivalence comparing two derived categories: the derived category of holonomic modules and derived category of modules…
Theory of weights in p-adic cohomology
Tomoyuki Abe, Daniel Caro
Let k be a finite field of characteristic p>0. We construct a theory of weights for overholonomic complexes of arithmetic D-modules with Frobenius structure on varieties over k. Th…
Langlands program for -adic coefficients and the petites camarades conjecture
Tomoyuki Abe
In this paper, we prove that, if Deligne's "petites camarades conjecture" holds, then a Langlands type correspondence holds also for -adic coefficients on a smooth curve over a…
Explicit calculation of Frobenius isomorphisms and Poincaré duality in the theory of arithmetic -modules
Tomoyuki Abe
The aim of this paper is to compute the Frobenius structures of some cohomological operators of arithmetic $\ms{D}$-modules. To do this, we calculate explicitly an isomorphism betw…
Rings of microdifferential operators for arithmetic -modules
Tomoyuki Abe
The aim of this paper is to develop a theory of microdifferential operators for arithmetic -modules. We first define the sheaves of microdifferential operators of arbi…
Product formula for p-adic epsilon factors
Tomoyuki Abe, Adriano Marmora
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…