Explicit calculation of Frobenius isomorphisms and Poincaré duality in the theory of arithmetic 𝒟-modules
Rendiconti del Seminario Matematico della Università di Padova, Tome 131 (2014), pp. 89-150 
@article{RSMUP_2014__131__89_0,
     author = {Abe, Tomoyuki},
     title = {Explicit calculation of {Frobenius} isomorphisms and {Poincar\'e} duality in the theory of arithmetic ${\mathcal {D}}$-modules},
     journal = {Rendiconti del Seminario Matematico della Universit\`a di Padova},
     pages = {89--150},
     year = {2014},
     publisher = {Seminario Matematico of the University of Padua},
     volume = {131},
     mrnumber = {3217753},
     zbl = {06329760},
     language = {en},
     url = {https://www.numdam.org/item/RSMUP_2014__131__89_0/}
}
TY  - JOUR
AU  - Abe, Tomoyuki
TI  - Explicit calculation of Frobenius isomorphisms and Poincaré duality in the theory of arithmetic ${\mathcal {D}}$-modules
JO  - Rendiconti del Seminario Matematico della Università di Padova
PY  - 2014
SP  - 89
EP  - 150
VL  - 131
PB  - Seminario Matematico of the University of Padua
UR  - https://www.numdam.org/item/RSMUP_2014__131__89_0/
LA  - en
ID  - RSMUP_2014__131__89_0
ER  - 
%0 Journal Article
%A Abe, Tomoyuki
%T Explicit calculation of Frobenius isomorphisms and Poincaré duality in the theory of arithmetic ${\mathcal {D}}$-modules
%J Rendiconti del Seminario Matematico della Università di Padova
%D 2014
%P 89-150
%V 131
%I Seminario Matematico of the University of Padua
%U https://www.numdam.org/item/RSMUP_2014__131__89_0/
%G en
%F RSMUP_2014__131__89_0
Abe, Tomoyuki. Explicit calculation of Frobenius isomorphisms and Poincaré duality in the theory of arithmetic ${\mathcal {D}}$-modules. Rendiconti del Seminario Matematico della Università di Padova, Tome 131 (2014), pp. 89-150. https://www.numdam.org/item/RSMUP_2014__131__89_0/

[Ab1] Abe T., Coherence of certain overconvergent isocrystals without Frobenius structures on curves, Math. Ann. 350, pp. 577–609 (2011). | Zbl | MR

[Ab2] Abe T., Langlands correspondence for isocrystals and existence of crystalline companion for curves, available at arxiv.org/abs/1310.0528.

[AC] Abe T. - Caro D., Theory of weights in p-adic cohomology, available at arxiv.org/abs/1303.0662.

[AM] Abe T. - Marmora A., On p-adic product formula for epsilon factors, To appear in J. Inst. Math. Jussieu. | MR

[BB] Baldassarri F. - Berthelot P., On Dwork cohomology for singular hypersurfaces, Geometric aspects of Dwork theory, vol. I, pp. 177–244, Walter de Gruyter (2004). | Zbl | MR

[BeP] Berthelot P., Cohomologie rigide et cohomologie rigide à supports propres. Première partie, preprint.

[Be1] Berthelot P., D-modules arithmétiques I. Opérateurs différentiels de niveau fini, Ann. Sci. École Norm. Sup. 4ème série, 29 no. 2, pp. 185–272 (1996). | Zbl | MR | Numdam

[Be2] Berthelot P., D-modules arithmétiques II. Descente par Frobenius, Mém. Soc. Math. Fr. 81 (2000). | Zbl | Numdam

[BeI] Berthelot P., Introduction à la théorie arithmétique des D-modules, Asterisque 279, pp. 1–80 (2002). | Zbl | MR | Numdam

[Ca1] Caro D., D-modules arithmétiques surcohérents. Application aux fonctions L, Ann. Inst. Fourier 54, pp. 1943–1996 (2005). | Zbl | MR | Numdam

[Ca2] Caro D., Fonctions L associées aux 𝒟 -modulles arithmétiques. Cas des courbes, Compos. Math. 142, pp. 169–206 (2006). | Zbl | MR

[Ca3] Caro D., Comparaison des foncteurs duaux des isocristaux surconvergents, Rend. Sem. Mat. Univ. Padova 114, pp. 131–211 (2006). | Zbl | MR | Numdam

[Ca4] Caro D., Dévissages des F-complexes de D-modules arithmétiques en F-isocristaux surconvergents, Invent. Math. 166 no. 2, pp. 397–456 (2006). | Zbl | MR

[Ca5] Caro D., 𝒟 -modules arithmétiques associés aux isocristaux survonvergents. Cas Lisse, Bull. Soc. Math. Fr. 137 no. 4, pp. 453–543 (2009). | Zbl | MR | Numdam

[Ca6] Caro D., 𝒟 -modules arithmétiques surholonomes, Ann. Sci. École Norm. Sup. 4ème série, 42 no. 1, pp. 141–192 (2009). | Zbl | MR | Numdam

[Ca7] Caro D., Sur la compatibilité à Frobenius de l’isomorphisme de dualité relative, Rend. Sem. Mat. Univ. Padova 122, pp. 235–286 (2009). | Zbl | MR | Numdam

[Co] Conrad, B., Grothendieck Duality and Base Change, Lecture Notes in Math.1750, Springer (2000). | Zbl | MR

[Cr] Crew R., Finiteness theorems for the cohomology of an overconvergent isocrystal on a curve, Ann. Sci. École Norm. Sup. 4ème série, 31 no. 6, pp. 717–763 (1998). | Zbl | MR | Numdam

[Ga] Garnier L., Descente par Frobenius explicite pour les 𝒟 † -modules, J. Algebra 205, pp. 542–577 (1998). | Zbl | MR

[GK] Gross B. - Koblitz N., Gauss sums and the p-adic Γ -function, Ann. Math. 109, pp. 569–581 (1979). | Zbl | MR

[Ha] Hartshorne R., Residues and Duality, Lecture Notes in Math. 20, Springer (1966). | Zbl | MR

[NH1] Noot-Huyghe C., Transformation de Fourier des 𝒟 -modules arithmétiques I, Geometric aspects of Dwork theory. vol. II, pp. 857–907, Walter de Gruyter (2004). | Zbl | MR

[NH2] Noot-Huyghe C., Finitude de la dimension homologique d’algèbres d’opérateurs différentiels faiblement complètes et à coefficients surconvergents, J. Algebra 307, pp. 499–540 (2007). | Zbl | MR

[Ka] Kashiwara M., Senkei-henbibun-houteishiki-kei no daisuuteki kenkyuu, Master thesis, Univ. of Tokyo (1970).

[Ke] Kedlaya K.S., Finiteness of rigid cohomology with coefficients, Duke Math. J. 134, pp. 15–97 (2006). | Zbl | MR

[Kl] Kleiman S.L., Relative duality for quasi-coherent sheaves, Compos. Math. 41, pp. 39–60 (1980). | Zbl | MR | Numdam

[St] Le Stum B., Rigid cohomology, Cambridge Tracts in Math. 172, Cambridge University Press (2007). | Zbl | MR

[Vi] Virrion A., Dualité locale et holonomie pour les D-modules arithmétiques, Bull. Soc. Math. Fr. 128, pp. 1–68 (2000). | Zbl | MR | Numdam

[Vi2] Virrion A., Trace et dualité relative pour les D-modules arithmétiques, Geometric aspects of Dwork theory. vol. II, pp. 1039–1112, Walter de Gruyter (2004). | Zbl | MR