Lang's theorem [SEP] named after
Lang's theorem
In algebraic geometry, Lang's theorem, introduced by Serge Lang, states: if "G" is a connected smooth algebraic group over a finite field formula_1, then, writing formula_2 for the Frobenius, the morphism of varieties
is surjective. Note that the kernel of this map (i.e., formula_4) is precisely formula_5.
The theorem implies that formula_6  
vanishes, and, consequently, any "G"-bundle on formula_7 is isomorphic to the trivial one. Also, the theorem plays a basic role
in the Battles of Second Manassas, Sharpsburg, and Antietam from Aug-Sep 1862. Colonel David Lang took over command of the Florida Brigade and led them at Fredricksburg in Dec 1862 and Chancellorsville in May 1863. Under Col. Lang's command the Florida Brigade fought at Gettysburg in July 1863. They were attached to Pickett's Division, and took part in the famous attack on the Union center on the 3rd day.
After the Battles of the Wilderness and Spotsylvania in 1864, the brigade was joined by the victors