Preliminary investigation of the extension

Note that, since Xa is normal and connected, it is irreducible. Put 

It is well-known (SGA 4 IX 2.2) that such a sheaf corresponds with an Stale covering of U. which we denote by the same letter F. Consider the normalization of SQ in the function ring R(F) of F this normalization is denoted by F11. We make the following two additional assumptions  

A sheaf F on UQ with property i) corresponds uniquely with a finite abelian group F on which n (U0, ) operates continuously  

F satisfies ii) iff this operation factors through by means of the homomorphism of (2.4.6 c). Therefore the sheaves F with property i), ii) and iii) correspond in a one to one manner with the finite abelian groups F on which operates continuously and which have order prime to the residue characteristics of SQ.  

2 it amounts to the same thing to give such a system (F ) or to 

Consider in the fetale topoloRy of sheaves of abelian groups F satisfying the following 3 properties  

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