Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Strongly semistable sheaves and the Mordell-Lang conjecture over
  function fields   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.

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The categories of this paper are: cs
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The categories of this paper are: hep-ph
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The categories of this paper are: physics
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The categories of this paper are: stat
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The categories of this paper are: solv-int
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The categories of this paper are: adap-org
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The categories of this paper are: astro-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: nlin
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The categories of this paper are: cond-mat
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The categories of this paper are: eess
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The categories of this paper are: atom-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: hep-lat
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The categories of this paper are: bayes-an