(Z)over-cap-SUBMODULES OF CURVES OVER FINITE FIELDS

作者：Kasparian Azniv^*

来源：Comptes Rendus de l Academie Bulgare des Sciences, 2012, 65(4): 437-440.

• divisor on a (Z)over-cap-submodule M of a curve over a finite field
• effective divisor
• linear equivalence of a divisor on M

Any smooth projective curve C of genus g, defined over a finite field F-q is acted by the absolute Galois group Gal((F-q) over bar /F-q) similar or equal to (Z) over cap = (lim) under left arrow (Z(n), +). For an arbitrary divisor D is an element of Div(C) of degree n %26gt;= 2g-1, Riemann-Roch Theorem implies that the effective divisors from the linear equivalence class of D constitute a projective space P(L(D)) = Pn-g(F-q). The present note introduces the notion of a divisor D on a (Z) over cap -submodule M of C. If the F-q-rational points M(F-q) of M do not deplete the F-q-rational points C(F-q) of C, then the effective divisors from the linear equivalence class of an arbitrary D is an element of Div(M) is shown to contain no projective subspaces P-k(F-q) of dimension k is an element of N over F-q. Let C-1, C-2 be smooth projective curves, defined over F-q, whose intersection C-1 boolean AND C-2 does not contain all F-q-rational points of C-1. Denote by O-C1 backslash C2* the units group of the ring O-C1 backslash C2 of the regular functions on C-1 backslash C-2. As an application of the main result, we show that the segments S-f = {g is an element of O-C1 backslash C2* vertical bar 0 %26lt;= (g)(infinity) %26lt;= (f)(infinity)} of f is an element of O-C1 backslash C2* do not contain an F-q-linear subspace of dimension %26gt;= 2.

• 出版日期2012