A fixed point formula for varieties over finite fields.
نویسندگان
چکیده
منابع مشابه
Abelian varieties over finite fields
A. Weil proved that the geometric Frobenius π = Fa of an abelian variety over a finite field with q = pa elements has absolute value √ q for every embedding. T. Honda and J. Tate showed that A 7→ πA gives a bijection between the set of isogeny classes of simple abelian varieties over Fq and the set of conjugacy classes of q-Weil numbers. Higher-dimensional varieties over finite fields, Summer s...
متن کاملZero-cycles on varieties over finite fields
For any field k, Milnor [Mi] defined a sequence of groups K 0 (k), K M 1 (k), K M 2 (k), . . . which later came to be known as Milnor K-groups. These were studied extensively by Bass and Tate [BT], Suslin [Su], Kato [Ka1], [Ka2] and others. In [Som], Somekawa investigates a generalization of this definition proposed by Kato: given semi-abelian varieties G1, . . . , Gs over a field k, there is a...
متن کاملSupersingular Abelian Varieties over Finite Fields
Let A be a supersingular abelian variety defined over a finite field k. We give an approximate description of the structure of the group A(k) of k-rational points of A in terms of the characteristic polynomial f of the Frobenius endomorphism of A relative to k. Write f = > gi i for distinct monic irreducible polynomials gi and positive integers ei . We show that there is a group homomorphism .:...
متن کامل2 Rationally Connected Varieties over Finite Fields
In this paper we study rationally connected varieties defined over finite fields. Then we lift these results to rationally connected varieties over local fields. Roughly speaking, a variety X over an algebraically closed field is rationally connected if it contains a rational curve through any number of assigned points P1, . . . , Pn. See [Kollár01a] for an introduction to their theory and for ...
متن کاملEndomorphisms of Abelian Varieties over Finite Fields
Almost all of the general facts about abelian varieties which we use without comment or refer to as "well known" are due to WEIL, and the references for them are [12] and [3]. Let k be a field, k its algebraic closure, and A an abelian variety defined over k, of dimension g. For each integer m > 1, let A m denote the group of elements aeA(k) such that ma=O. Let l be a prime number different fro...
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: MATHEMATICA SCANDINAVICA
سال: 1978
ISSN: 1903-1807,0025-5521
DOI: 10.7146/math.scand.a-11747