The Chevalley-Warning theorem and a combinatorial question on finite groups
نویسندگان
چکیده
منابع مشابه
Exponential sums and the Chevalley-Warning theorem
These notes consist of an expanded version of a talk at the Michigan Number Theory Day on November 12, 2010.
متن کاملA Proof of the Barsotti-Chevalley Theorem on Algebraic Groups
A fundamental theorem of Barsotti and Chevalley states that every smooth connected algebraic group over a perfect field is an extension of an abelian variety by a smooth affine algebraic group. In 1956 Rosenlicht gave a short proof of the theorem. We explain his proof in the language of modern algebraic geometry.
متن کاملSome combinatorial aspects of finite Hamiltonian groups
In this paper we provide explicit formulas for the number of elements/subgroups/cyclic subgroups of a given order and for the total number of subgroups/cyclic subgroups in a finite Hamiltonian group. The coverings with three proper subgroups and the principal series of such a group are also counted. Finally, we give a complete description of the lattice of characteristic subgroups of a finite H...
متن کاملA Note on the Chevalley–Warning Theorems
The most widely known result of Chevalley–Warning type states that if one has a polynomial over a finite field of characteristic p, and the number of variables exceeds the degree, then the number of zeros is a multiple of p. In particular, if the polynomial is homogeneous, there is at least one non-trivial zero. There are a number of related results in the literature. Generally, let Fq be a fin...
متن کاملFe b 20 08 A WEAK CHEVALLEY - WARNING THEOREM FOR QUASI - FINITE FIELDS
There exists a function f : N → N such that for every positive integer d, every quasi-finite field K and every projective hypersurface X of degree d and dimension ≥ f(d), the set X(K) is non-empty. This is a special case of a more general result about intersections of hypersurfaces of fixed degree in projective spaces of sufficiently high dimension over fields with finitely generated Galois gro...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1999
ISSN: 0002-9939,1088-6826
DOI: 10.1090/s0002-9939-99-04704-8