Incidence coalgebras of intervally finite posets, their integral quadratic forms and comodule categories

Daniel Simson

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In the classical Witt theory over a field F, the study of quadratic forms begins with two simple invariants: the dimension of a form modulo 2, called the dimension index and denoted e⁰: W(F) → ℤ/2, and the discriminant e¹ with values in k₁(F) = F*/F*², which behaves well on the fundamental ideal I(F)= ker(e⁰). Here a more sophisticated situation is considered, of quadratic forms over a scheme and, more generally, over an exact category with duality. Our purposes are: ...