Notes on isocrystals

Kedlaya, Kiran S.

doi:10.1016/j.jnt.2021.12.004

Cited by 6 publications

(6 citation statements)

References 82 publications

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“…By assertion , it suffices to prove the assertion for convergent -isocrystals. By [Ked22a, Theorem 5.3] and a similar argument as in assertion , it suffices to show its fullness.…”

Section: Drinfeld's Lemma For Convergent -Isocrystalsmentioning

confidence: 98%

“…There exists a slope filtration as convergent -isocrystals [Ked22a, Corollary 4.2]. It suffices to show that each partial Frobenius preserves this filtration, that is the composition vanishes.…”

Section: Drinfeld's Lemma For Convergent -Isocrystalsmentioning

confidence: 99%

“…We claim that there exists an overconvergent isocrystal of extending such that . By Kedlaya and Shiho's purity theorem [Ked22a, Theorem 5.1], we may assume that the boundary is a smooth divisor. Since the local monodromy of around is constant [Ked07, Theorem 5.2.1], then so is the local monodromy of around .…”

Section: Drinfeld's Lemma For Overconvergent -Isocrystalsmentioning

confidence: 99%

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Drinfeld's lemma for F-isocrystals, II: Tannakian approach

Kedlaya,

2023

Compositio Math.

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“…By assertion , it suffices to prove the assertion for convergent -isocrystals. By [Ked22a, Theorem 5.3] and a similar argument as in assertion , it suffices to show its fullness.…”

Section: Drinfeld's Lemma For Convergent -Isocrystalsmentioning

confidence: 98%

Section: Drinfeld's Lemma For Convergent -Isocrystalsmentioning

confidence: 99%

Section: Drinfeld's Lemma For Overconvergent -Isocrystalsmentioning

confidence: 99%

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Drinfeld's lemma for F-isocrystals, II: Tannakian approach

Kedlaya,

2023

Compositio Math.

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“…Let F-Isoc(X) be the category of F -isocrystals over X (as defined for example in [Mor19,§ A.1]). By [Ked22,Corollary 4.2], every F -isocrystal E with constant Newton polygon admits a slope filtration…”

Section: Proof Of Proposition 3231mentioning

confidence: 99%

“…Let be the category of -isocrystals over (as defined for example in [Mor19, § A.1]). By [Ked22, Corollary 4.2], every -isocrystal with constant Newton polygon admits a slope filtration such that is isoclinic of some slope with . By [BBM82], there is a fully faithful contravariant functor .…”

Section: On the Injectivity Of The éTale Abel–jacobi Mapmentioning

confidence: 99%

Perfect points of abelian varieties

Ambrosi

2023

Compositio Math.

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Let $p$ be a prime number, $k$ a finite field of characteristic $p>0$ and $K/k$ a finitely generated extension of fields. Let $A$ be a $K$ -abelian variety such that all the isogeny factors are neither isotrivial nor of $p$ -rank zero. We give a necessary and sufficient condition for the finite generation of $A(K^{\mathrm {perf}})$ in terms of the action of $\mathrm {End}(A)\otimes \mathbb {Q}_p$ on the $p$ -divisible group $A[p^{\infty }]$ of $A$ . In particular, we prove that if $\mathrm {End}(A)\otimes \mathbb {Q}_p$ is a division algebra, then $A(K^{\mathrm {perf}})$ is finitely generated. This implies the ‘full’ Mordell–Lang conjecture for these abelian varieties. In addition, we prove that all the infinitely $p$ -divisible elements in $A(K^{\mathrm {perf}})$ are torsion. These reprove and extend previous results to the non-ordinary case.

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Minimal slope conjecture of F-isocrystals

Tsuzuki

2022

Invent. math.

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Notes on isocrystals

Cited by 6 publications

References 82 publications

Drinfeld's lemma for F-isocrystals, II: Tannakian approach

Drinfeld's lemma for F-isocrystals, II: Tannakian approach

Perfect points of abelian varieties

Minimal slope conjecture of F-isocrystals

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