The rank two p-curvature conjecture on generic curves

Patel, Anand; Shankar, Ananth N.; Whang, Junho Peter

doi:10.1016/j.aim.2021.107800

Cited by 5 publications

(3 citation statements)

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“…Conjecture 8.3 (Ekedahl, Shepherd-Barron, and Taylor). Let F be a holomorphic foliation on a projective manifold X with an integral model (X , F ) defined over a finitely generated Z-algebra R. [40,36].…”

Section: 2mentioning

confidence: 99%

Codimension one foliations in positive characteristic

Mendson¹,

Pereira²

2022

Preprint

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We investigate the geometry of codimension one foliations on smooth projective varieties defined over fields of positive characteristic with an eye toward applications to the structure of codimension one holomorphic foliations on projective manifolds. CONTENTS 1. Introduction 1 2. Distributions and foliations 2 Part 1. Geometry of foliations in positive characteristic 4 3. Differential geometry in positive characteristic 4 4. Particular features of foliations in positive characteristic 7 5. Degeneracy divisor of the p-curvature 13 6. Families of foliations 22 7. Integrability of the Cartier transform 24 8. Lifting the kernel of the p-curvature 26 Part 2. The space of holomorphic foliations on projective spaces 29 9. Foliations on complex projective spaces 29 10. Subdistributions of minimal degree 31 11. Codimension two subdistributions of small degree 34 12. Foliations without subdistributions of small degree 40 References 42

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Section: 2mentioning

confidence: 99%

Codimension one foliations in positive characteristic

Mendson¹,

Pereira²

2022

Preprint

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“…(Note here that each component of †jc 0 has positive genus, by design.) We shall prove that j † 00 is finite, so a fortiori has finite monodromy along c. For this, we follow the strategy of [20] below.…”

Section: Proof Of Theorem Amentioning

confidence: 99%

“…Acknowledgements Theorems A and B along with parts of this paper originally appeared in Chapter 6 of Whang's PhD thesis [29], but the proof had a gap which has been filled in this paper. Whang thanks Peter Sarnak and Phillip Griffiths for encouragement, and Anand Patel and Ananth Shankar for collaborative work in [20], We thank the anonymous referee for a careful reading and useful comments. Biswas and Mj are supported in part by the Department of Atomic Energy, Government of India, under project 12-R&D-TFR-5.01-0500.…”

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confidence: 99%

Surface group representations in SL2(ℂ) with finite mapping class orbits

Biswas

Gupta

et al. 2022

Geom. Topol.

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Given an oriented surface of positive genus with finitely many punctures, we classify the finite orbits of the mapping class group action on the moduli space of semisimple complex special linear two dimensional representations of the fundamental group of the surface. For surfaces of genus at least two, such orbits correspond to homomorphisms with finite image. For genus one, they correspond to the finite or special dihedral representations. We also obtain an analogous result for bounded orbits in the moduli space. 57M50; 57M05, 20E36, 20F29 1. Introduction 679 2. Background 683 3. Non-Zariski-dense representations 690 4. Analysis of Dehn twists 696 5. Proof of the main results 701 6. Applications 712 Appendix Case of a once-punctured torus 713 References 717

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Lecture 2: Kronecker’s Rationality Criteria and Grothendieck’s p-Curvature Conjecture

Esnault

2023

Lecture Notes in Mathematics

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The rank two p-curvature conjecture on generic curves

Cited by 5 publications

References 10 publications

Codimension one foliations in positive characteristic

Codimension one foliations in positive characteristic

Surface group representations in SL2(ℂ) with finite mapping class orbits

Lecture 2: Kronecker’s Rationality Criteria and Grothendieck’s p-Curvature Conjecture

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