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Strongly semistable sheaves and the Mord...

Rössler, Damian...

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Strongly semistable sheaves and the Mordell-Lang conjecture over function fields by Rössler, Damian ( Author )

Content Provider	Lemonjar Open Access
Publisher	Australian National University
Publication Date	06-09-2023
Summary	We give a new proof of the Mordell-Lang conjecture in positive characteristic, in the situation where the variety under scrutiny is a smooth subvariety of an abelian variety. Our proof is based on the theory of semistable sheaves in positive characteristic, in particular on Langer's theorem that the Harder-Narasimhan filtration of sheaves becomes strongly semistable after a finite number of iterations of Frobenius pull-backs. The interest of this proof is that it provides simple effective bounds (depending on the degree of the canonical line bundle) for the degree of the isotrivial finite cover whose existence is predicted by the Mordell-Lang conjecture. We also present a conjecture on the Harder-Narasimhan filtration of the cotangent bundle of a smooth projective variety of general type in positive characteristic and a conjectural refinement of the Bombieri-Lang conjecture in positive characteristic.
ISBN	-
Item Type	Article
File Type	pdf
File Size	29.34 KB
Language	English
Subjects	-
Unlimited	MYR 0.01
Total read	-
URL	http://arxiv.org/abs/1412.7303

Citation

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AMA 11th EditionReferences

Rössler, Damian. Strongly semistable sheaves and the Mordell-Lang conjecture over function fields. Australian National University. September 06, 2023. Accessed November 01, 2024. https://online.provdatabase.com/cite/24120

APA 7th EditionReferences

Rössler, Damian. (2023). Strongly semistable sheaves and the Mordell-Lang conjecture over function fields. Australian National University. https://online.provdatabase.com/cite/24120

Chicago 17th EditionReferences

Rössler, Damian. Strongly semistable sheaves and the Mordell-Lang conjecture over function fields. Australian National University. 2023. https://online.provdatabase.com/cite/24120

HarvardReferences

Rössler, Damian. (2023). Strongly semistable sheaves and the Mordell-Lang conjecture over function fields. [Online]. Australian National University. Available from: https://online.provdatabase.com/cite/24120. (Accessed 01 November 2024).

Harvard AustraliaReferences

Rössler, Damian, 2023, Strongly semistable sheaves and the Mordell-Lang conjecture over function fields, Australian National University, viewed 01 November 2024, <https://online.provdatabase.com/cite/24120>

MLA 9th EditionWorks Cited

Rössler, Damian. Strongly semistable sheaves and the Mordell-Lang conjecture over function fields. Australian National University, 2023. PROV Database, https://online.provdatabase.com/cite/24120.

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