منابع مشابه
Multiple Zeta Values over Global Function Fields
Abstract. Let K be a global function field with finite constant field Fq of order q. In this paper we develop the analytic theory of a multiple zeta function Zd(K; s1, . . . , sd) in d independent complex variables defined over K. This is the function field analog of the Euler-Zagier multiple zeta function ζd(s1, . . . , sd) of depth d ([Z1]). Our main result is that Zd(K; s1, . . . , sd) has a...
متن کاملWitt Equivalence of Function Fields over Global Fields
Witt equivalent fields can be understood to be fields having the same symmetric bilinear form theory. Witt equivalence of finite fields, local fields and global fields is well understood. Witt equivalence of function fields of curves defined over archimedean local fields is also well understood. In the present paper, Witt equivalence of general function fields over global fields is studied. It ...
متن کاملFiniteness properties of soluble arithmetic groups over global function fields
Let G be a Chevalley group scheme and B ≤ G a Borel subgroup scheme, both defined over Z. Let K be a global function field, S be a finite non-empty set of places over K , and OS be the corresponding S–arithmetic ring. Then, the S– arithmetic group B(OS) is of type F |S|−1 but not of type FP |S| . Moreover one can derive lower and upper bounds for the geometric invariants Σ(B(OS)). These are sha...
متن کاملIwasawa Theory of Zp-Extensions over Global Function Fields
In this paper we study the Iwasawa theory of Zp-extensions of global function fields k over finite fields of characteristic p. When d = 1 we first show that Iwasawa invariants are well defined under the assumption that only finitely many primes are ramified in the extension, then we prove that the Iwasawa μ-invariant can be arbitrarily large for some extension of any given base field k. After g...
متن کاملUniversal Norms on Abelian Varieties over Global Function Fields
We examine the Mazur-Tate canonical height pairing defined between an abelian variety over a global field and its dual. By expressing local factors of this pairing in terms of nonarchimedean theta functions, we show in the case of global function fields that certain of these pairings are annihilated by universal norms coming from Carlitz cyclotomic extensions. Furthermore, for elliptic curves w...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2016
ISSN: 0002-9939,1088-6826
DOI: 10.1090/proc/13265