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On the F-fundamental group scheme

✍ Scribed by Sanjay Amrutiya; Indranil Biswas

Publisher
Elsevier Science
Year
2010
Tongue
French
Weight
164 KB
Volume
134
Category
Article
ISSN
0007-4497

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✦ Synopsis

Let X be a smooth projective variety defined over a perfect field k of positive characteristic, and let F X be the absolute Frobenius morphism of X. For any vector bundle E -β†’ X, and any polynomial g with non-negative integer coefficients, define the vector bundle g(E) using the powers of F X and the direct sum operation. We construct a neutral Tannakian category using the vector bundles with the property that there are two distinct polynomials f and g with non-negative integer coefficients such that f (E) = g(E). We also investigate the group scheme defined by this neutral Tannakian category.

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