NOTATIONS FREQUENTLY USED Con R/S: conorm from R to S (IV, 7). Cosp R/S: cotrace from R to £ (for repartitions, IV, 7 for differentials, VI, 2 and VI, 6). d(a): degree of a divisor a (I, 7). b(x): divisor of an element x (I, 8). b(w): divisor of a differential w (II, 6). 5(a): dimension of the space of differentials which are multiple of a divisor a (II, 5). d: boundary (VII, 3). Hn{X, Y): n-dimensional homology group of X modulo Y (VII, 3). *(T V): intersection numbers of the 1-chains y and y' (VII, 6). j(«,«'):(VII,5). K("-): field obtained by adjunction to the field K of the element or elements or set of elements whose symbols are between the sign ( and the sign ) special meaning for fields of algebraic functions of one variable defined in V, 4. 1(a): dimension of the space of elements which are multiples of a divisor a (II, 1). vp: order function at a place p (for elements, I, 5 and III, 1 for repartitions, II, 4 for differentials, II, 6). Ns/R: Norm from S to R (IV, 7). #L:(IV,5). W * .-^-component of a differential w (II, 7). res *!: residue of a differential w at a place p (III, 5). Spa/*: Trace from S to R (for repartitions, IV, 7 for differentials, VI, 2). Sp?/«: (IV, 5). | 7 |: set of points of a chain 7 (VII, 3). Xlll
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