Linear Chevalley Estimates

A Chevalley-Warning Approach to P-adic Estimates of Character Sums

A Differential Chevalley Theorem

We prove a differential analog of a theorem of Chevalley on extending homomorphisms for rings with commuting derivations, generalizing a theorem of Kac. As a corollary, we establish that, under suitable hypotheses, the image of a differential scheme under a finite morphism is a constructible set. We also obtain a new algebraic characterization of differentially closed fields. We show that simil...

Tight Bounds for Chevalley--warning--ax--katz Type Estimates, with Improved Applications

In 1935, C. Chevalley proved a conjecture by E. Artin: if F ðX1; . . . ; XmÞ is a homogeneous polynomial of total degree d < m over a 7nite 7eld Fq having q 1⁄4 p elements, then F has a non-trivial zero. Chevalley showed the result to hold even when the homogeneity hypothesis is replaced by the weaker requirement that F ðX1; . . . ; XmÞ has no constant term. Almost immediately, E. Warning showe...

The Real Chevalley Involution

Theorem (1) There is an involution C of G satisfying: C(h) = h −1 (h ∈ H); (2) C(g) ∼ g −1 for all semisimple elements g; (3) Any two such involutions are conjugate by an inner automorphism;

Lectures on Chevalley Groups

( b ) H is maximal n i l p o t e n t and every subgroup of f i n i t e l a d e x . . i s of f i n i t e index i n i t s normalizer. Proof of Theorem 6: ( a ) Map Ga -> #, by x,: t -> x,(t) . This is a r a t i o n a l homomorphism. So s i n c e Ga i s a connected , ~ g e b r a i c group s o i s Xa . Hence G is a lgebra ic and connected.. Let R = r a d G . Since R is so lvable and normal it i s f...