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Homological Equivalences of Modules and Their Projective Invariants
Author(s) -
Holland David
Publication year - 1991
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/s2-43.3.396
Subject(s) - mathematics , pure mathematics , automorphism , endomorphism , invariant (physics) , galois group , endomorphism ring , fundamental theorem of galois theory , abelian extension , algebra over a field , discrete mathematics , mathematical physics
This paper generalises Chinburg's construction [ 4 , 5 ] of invariants in the class group of an integral group ring from two‐fold extensions of (Galois) modules. The two main results are the expression of invariants of endomorphisms of a non‐projective lattice over an order (which lie in the kernel group) in terms of reduced norms of local automorphisms, and the description of a coset of the Swan subgroup of the class group, which contains Chinburg's invariant Ω( N / K , 1) of a finite Galois extension N/K of number fields, in terms of invariants of homomorphisms.