{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:TYB5PZDHGCQTADGZPDJKBEGHY5","short_pith_number":"pith:TYB5PZDH","schema_version":"1.0","canonical_sha256":"9e03d7e46730a1300cd978d2a090c7c74df2d0abf0a2482bcd8db1c803755da5","source":{"kind":"arxiv","id":"1701.00252","version":1},"attestation_state":"computed","paper":{"title":"Semistability of Rational Principal $GL_n$-Bundles in Positive Characteristic","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Lingguang Li","submitted_at":"2017-01-01T15:47:17Z","abstract_excerpt":"Let $k$ be an algebraically closed field of characteristic $p>0$, $X$ a smooth projective variety over $k$ with a fixed ample divisor $H$. Let $E$ be a rational $GL_n(k)$-bundle on $X$, and $\\rho:GL_n(k)\\rightarrow GL_m(k)$ a rational $GL_n(k)$-representation at most degree $d$ such that $\\rho$ maps the radical $R(GL_n(k))$ of $GL_n(k)$ into the radical $R(GL_m(k))$ of $GL_m(k)$. We show that if $F_X^{N*}(E)$ is semistable for some integer $N\\geq\\max\\limits_{00$, $X$ a smooth projective variety over $k$ with a fixed ample divisor $H$. Let $E$ be a rational $GL_n(k)$-bundle on $X$, and $\\rho:GL_n(k)\\rightarrow GL_m(k)$ a rational $GL_n(k)$-representation at most degree $d$ such that $\\rho$ maps the radical $R(GL_n(k))$ of $GL_n(k)$ into the radical $R(GL_m(k))$ of $GL_m(k)$. We show that if $F_X^{N*}(E)$ is semistable for some integer $N\\geq\\max\\limits_{0