, In loc. it. indeed, a similar bound was obtained for -adic nearby slopes of smooth morphisms [Tey15]. In that setting, the main tools are Beilinson's and Saito's work on the singular support [Bei16] and the characteristic cycle [Sai17] for -adic sheaves, as well as semi-continuity properties

, From this perspective, proposition 5.1.2 is a positive answer to a local variant for differential equations of a conjecture in [Lea16] on the ramification of the étale cohomology groups for local systems on the generic fiber of a strictly semi

Y. André, Structure des connexions méromorphes formelles de plusieurs variables et semi-continuité de l'irrégularité, Invent. math, vol.170, 2007.

A. Abbes and T. Saito, Ramification of local fields with imperfect residue fields, Amer. J. Math, vol.124, 2002.

A. Beilinson, Constructible sheaves are holonomic, Sel. Math. New. Ser, vol.22, 2016.

A. Borel, Linear Algebraic Groups, Graduate Texts in Mathematics, 1991.

D. G. Babbitt and V. S. Varadarajan, Local Moduli For Meromorphic Differential Equations, pp.169-170, 1989.

G. Cotti, B. Dubrovin, and D. Guzzetti, Isomonodromy deformations at an irregular singularity with coalescing eigenvalues, 2017.

P. Deligne, Equations différentielles à points singuliers réguliers, Lecture Notes in Mathematics, vol.163, 1970.

. Lettre-À-malgrange, Singularités irrégulières, vol.5, 1983.

H. Esnault and M. Kerz, A finiteness theorem for Galois representations of function fields over finite fields (after Deligne), Acta Mathematica Vietnamica, vol.4, 2012.

J. Frenkel, Cohomologie non abélienne et espaces fibrés, Bulletin de la S.M.F, vol.85, 1957.

H. Hu and E. Yang, Semi-continuity for total dimension divisors of étale sheaves, Internat. J. Math, vol.28, 2017.

M. Hien, Periods for flat algebraic connections, Inventiones Mathematicae, vol.178, 2009.

H. Hu and J. Teyssier, Characteristic cycle and wild ramification for nearby cycles of étale sheaves, 2018.

H. Hu, Logarithmic ramifications of étale sheaves by restricting to curves, IMRN rnx228, 2017.

M. Kashiwara, Index theorem for a maximally overdetermined system of linear differential equations, Proc. Jap Acad, pp.49-59, 1973.

, On the maximally overdetermined systems of linear differential equations I, Publ. RIMS, vol.10, 1975.

, Vanishing cycle sheaves and holonomic systems of differential equations, Algebraic Geometry, Lecture Notes in Mathematics, vol.1016, 1983.

, Algebraic study of systems of partial differential equations, Mémoire de la SMF, vol.63, 1970.

K. Kedlaya, Good formal structures for flat meromorphic connections I: Surfaces, Duke Math, J, vol.154, 2010.

, Good formal structures for flat meromorpohic connexions II: excellent schemes, J. Amer. Math. Soc, vol.24, 2011.

, Good formal structures for flat meromorphic connections, III: Irregularity and turning loci, 2018.

M. Kashiwara and P. Schapira, Sheaves on manifolds, 1990.

G. Laumon, Transformation de Fourier, constantes d'équations fonctionnelles et conjecture de Weil, 1987.
DOI : 10.1007/bf02698937
URL : http://www.numdam.org/article/PMIHES_1987__65__131_0.pdf

I. Leal, On the ramification of étale cohomology groups, J. reine angew. Math, 2016.

B. Malgrange, Rapport sur les théorèmes d'indice de Boutet de Monvel et Kashiwara, Analyse et topologie sur les espaces singuliers II-III, vol.101, 1981.

, La classification des connections irrégulières à une variable, vol.37, 1983.

P. De-bernstein-sato, Astérisque, pp.101-102, 1983.

, Connexions méromorphes 2: Le réseau canonique, Inv. Math, vol.124, 1996.

Z. Mebkhout, Le formalisme des six opérations de Grothendieck pour les Dmodules cohérents, vol.35, 1989.

, Le théorème de positivité de l'irrégularité pour les DX -modules, The Grothendieck Festschrift III, vol.88, 1990.

L. De-positivité, . Le-théorème-de-comparaison, and . Le-théorème-d'existence-de-riemann, Éléments de la théorie des systèmes différentiels géométriques, Séminaires et Congrès, vol.8, 2004.

P. Maisonobe and Z. Mebkhout, Le théorème de comparaison pour les cycles évanescents, Éléments de la théorie des systèmes différentiels géométriques, Séminaires et Congrès, vol.8, 2004.

T. Mochizuki, Good formal structure for meromorphic flat connections on smooth projective surfaces., Algebraic analysis and around in honor of Professor Masaki Kashiwara's 60th birthday, 2009.
DOI : 10.2969/aspm/05410223
URL : https://doi.org/10.2969/aspm/05410223

, The Stokes structure of a good meromorphic flat bundle, Journal of the Institute of Mathematics of Jussieu, vol.10, 2011.

, Wild Harmonic Bundles and Wild Pure Twistor D-modules, vol.340, 2011.

C. Sabbah, Equations différentielles à points singuliers irréguliers et phénomène de Stokes en dimension 2, Astérisque, vol.263, 2000.
DOI : 10.5802/aif.1386
URL : http://archive.numdam.org/article/AIF_1993__43_5_1619_0.pdf

, Déformations isomonodromiques et variétés de Frobenius, Savoirs actuels, vol.2060, 2002.

, A remark on the Irregularity Complex, Journal of Singularities, vol.16, 2017.

, Deformations and degenerations of irregular singularities, 2017.

T. Saito, The characteristic cycle and the singular support of a constructible sheaf, Invent. Math, vol.207, issue.2, 2017.

C. Simpson, Moduli of representations of the fundamental group of a smooth projective variety II, Publ. Math. de l'IHES, vol.80, 1994.

, Stack Project, ch. Descent

M. Singer and M. Van-der-put, Galois Theory of Linear Differential Equations, Grundlehren der mathematischen Wissenschaften, vol.328, 2000.

J. Teyssier, Autour de l'irrégularité des connexions méromorphes, 2013.

C. Mail and . Sabbah, , 2014.

, Nearby slopes and boundedness for -adic sheaves in positive characteristic, 2015.

, A boundedness theorem for nearby slopes of holonomic D-modules, Compositio Mathematica, vol.152, 2016.

, Skeletons and moduli of Stokes torsors, To appear at Annales Scientifiques de l'Ecole Normale Supérieure, 2017.

, Higher dimensional Stokes structures are rare, 2019.

J. Teyssier,