Langlands program for p-adic coefficients and the petits camarades conjecture
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Tomoyuki Abe
Abstract
In this paper, we prove that, if Deligne’s “petits camarades conjecture” holds, then a Langlands type correspondence holds also for p-adic coefficients on a smooth curve over a finite field. As an application, we prove that any overconvergent F-isocrystal of rank less than or equal to 2 on a smooth curve is ι-mixed.
Funding statement: This work was supported by Grant-in-Aid for Research Activity Start-up 23840006.
Acknowledgements
The author would like to thank Professors N. Tsuzuki and A. Shiho for various discussions and giving him some ideas. He would also like to express his gratitude to Professor T. Saito for giving him some valuable advice and encouragements.
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© 2018 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- The equivariant Tamagawa number conjecture and the extended abelian Stark conjecture
- Langlands program for p-adic coefficients and the petits camarades conjecture
- Existence and uniqueness of minimizers of general least gradient problems
- Partial regularity for mass-minimizing currents in Hilbert spaces
- Which abelian tensor categories are geometric?
- On Mordell–Weil groups and congruences between derivatives of twisted Hasse–Weil L-functions
- Compactness properties for geometric fourth order elliptic equations with application to the Q-curvature flow
- Compact operators and algebraic K-theory for groups which act properly and isometrically on Hilbert space
Artikel in diesem Heft
- Frontmatter
- The equivariant Tamagawa number conjecture and the extended abelian Stark conjecture
- Langlands program for p-adic coefficients and the petits camarades conjecture
- Existence and uniqueness of minimizers of general least gradient problems
- Partial regularity for mass-minimizing currents in Hilbert spaces
- Which abelian tensor categories are geometric?
- On Mordell–Weil groups and congruences between derivatives of twisted Hasse–Weil L-functions
- Compactness properties for geometric fourth order elliptic equations with application to the Q-curvature flow
- Compact operators and algebraic K-theory for groups which act properly and isometrically on Hilbert space
