@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}, volume = {132}, year = {2014}, pages = {89-150}, mrnumber = {3217753}, zbl = {06329760}, language = {en}, url = {http://dml.mathdoc.fr/item/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 132 (2014) pp. 89-150. http://gdmltest.u-ga.fr/item/RSMUP_2014__131__89_0/
[Ab1] Coherence of certain overconvergent isocrystals without Frobenius structures on curves, Math. Ann. 350, pp. 577–609 (2011). | MR 2805637 | Zbl 1264.12005
,[Ab2] Langlands correspondence for isocrystals and existence of crystalline companion for curves, available at arxiv.org/abs/1310.0528.
,[AC] Theory of weights in p-adic cohomology, available at arxiv.org/abs/1303.0662.
- ,[AM] On p-adic product formula for epsilon factors, To appear in J. Inst. Math. Jussieu. | MR 3315058
- ,[BB] On Dwork cohomology for singular hypersurfaces, Geometric aspects of Dwork theory, vol. I, pp. 177–244, Walter de Gruyter (2004). | MR 2023290 | Zbl 1117.14022
- ,[BeP] Cohomologie rigide et cohomologie rigide à supports propres. Première partie, preprint.
,[Be1] D-modules arithmétiques I. Opérateurs différentiels de niveau fini, Ann. Sci. École Norm. Sup. 4ème série, 29 no. 2, pp. 185–272 (1996). | Numdam | MR 1373933 | Zbl 0886.14004
,[Be2] D-modules arithmétiques II. Descente par Frobenius, Mém. Soc. Math. Fr. 81 (2000). | Numdam | Zbl 0948.14017
,[BeI] Introduction à la théorie arithmétique des D-modules, Asterisque 279, pp. 1–80 (2002). | MR 1922828 | Zbl 1098.14010
,[Ca1] D-modules arithmétiques surcohérents. Application aux fonctions L, Ann. Inst. Fourier 54, pp. 1943–1996 (2005). | Numdam | MR 2134230 | Zbl 1129.14030
,[Ca2] Fonctions L associées aux -modulles arithmétiques. Cas des courbes, Compos. Math. 142, pp. 169–206 (2006). | MR 2197408 | Zbl 1167.14012
,[Ca3] Comparaison des foncteurs duaux des isocristaux surconvergents, Rend. Sem. Mat. Univ. Padova 114, pp. 131–211 (2006). | Numdam | MR 2207865 | Zbl 1165.14305
,[Ca4] Dévissages des F-complexes de D-modules arithmétiques en F-isocristaux surconvergents, Invent. Math. 166 no. 2, pp. 397–456 (2006). | MR 2249804 | Zbl 1114.14011
,[Ca5] -modules arithmétiques associés aux isocristaux survonvergents. Cas Lisse, Bull. Soc. Math. Fr. 137 no. 4, pp. 453–543 (2009). | Numdam | MR 2572180 | Zbl 1300.14021
,[Ca6] -modules arithmétiques surholonomes, Ann. Sci. École Norm. Sup. 4ème série, 42 no. 1, pp. 141–192 (2009). | Numdam | MR 2518895 | Zbl 1168.14013
,[Ca7] Sur la compatibilité à Frobenius de l’isomorphisme de dualité relative, Rend. Sem. Mat. Univ. Padova 122, pp. 235–286 (2009). | Numdam | MR 2582839 | Zbl 05663015
,[Co] Grothendieck Duality and Base Change, Lecture Notes in Math.1750, Springer (2000). | MR 1804902 | Zbl 0992.14001
,[Cr] 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). | Numdam | MR 1664230 | Zbl 0943.14008
,[Ga] Descente par Frobenius explicite pour les -modules, J. Algebra 205, pp. 542–577 (1998). | MR 1632769 | Zbl 0926.12006
,[GK] Gauss sums and the p-adic -function, Ann. Math. 109, pp. 569–581 (1979). | MR 534763 | Zbl 0406.12010
- ,[Ha] Residues and Duality, Lecture Notes in Math. 20, Springer (1966). | MR 222093 | Zbl 0212.26101
,[NH1] Transformation de Fourier des -modules arithmétiques I, Geometric aspects of Dwork theory. vol. II, pp. 857–907, Walter de Gruyter (2004). | MR 2099091 | Zbl 1126.14016
,[NH2] Finitude de la dimension homologique d’algèbres d’opérateurs différentiels faiblement complètes et à coefficients surconvergents, J. Algebra 307, pp. 499–540 (2007). | MR 2275360 | Zbl 1111.14006
,[Ka] Senkei-henbibun-houteishiki-kei no daisuuteki kenkyuu, Master thesis, Univ. of Tokyo (1970).
,[Ke] Finiteness of rigid cohomology with coefficients, Duke Math. J. 134, pp. 15–97 (2006). | MR 2239343 | Zbl 1133.14019
,[Kl] Relative duality for quasi-coherent sheaves, Compos. Math. 41, pp. 39–60 (1980). | Numdam | MR 578050 | Zbl 0403.14003
,[St] Rigid cohomology, Cambridge Tracts in Math. 172, Cambridge University Press (2007). | MR 2358812 | Zbl 1131.14001
,[Vi] Dualité locale et holonomie pour les D-modules arithmétiques, Bull. Soc. Math. Fr. 128, pp. 1–68 (2000). | Numdam | MR 1765829 | Zbl 0955.14015
,[Vi2] Trace et dualité relative pour les D-modules arithmétiques, Geometric aspects of Dwork theory. vol. II, pp. 1039–1112, Walter de Gruyter (2004). | MR 2099095 | Zbl 1083.14017
,