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- Title
Semistability of Frobenius Direct Image of Representations of Cotangent Bundles.
- Authors
Li, Ling Guang
- Abstract
Let k be an algebraically closed field of characteristic p > 0, X a smooth projective variety over k with a fixed ample divisor H, FX : X → X the absolute Frobenius morphism on X. Let E be a rational GLn(k)-bundle on X, and ρ : GLn(k) → GLm(k) a rational GLn(k)-representation of degree at most d such that ρ maps the radical RGLn(k)) of GLn(k) into the radical R(GLm(k)) of GLm(k). We show that if FXN*(E) is semistable for some integer N≥max0<r<m(rm)⋅logp(dr), then the induced rational GLm(k)-bundle E(GLm(k)) is semistable. As an application, if dimX = n, we get a sufficient condition for the semistability of Frobenius direct image FX*(ρ*(ΩX1)), where ρ*(ΩX1) is the vector bundle obtained from ΩX1 via the rational representation ρ.
- Subjects
COTANGENT function; FROBENIUS algebras; MATHEMATICAL constants; HEAT equation; FOURIER transforms
- Publication
Acta Mathematica Sinica, 2018, Vol 34, Issue 11, p1677
- ISSN
1439-8516
- Publication type
Article
- DOI
10.1007/s10114-018-8078-6