8 papers
Stickelberger's discriminant theorem for algebras
Asher Auel, Owen Biesel, John Voight
Stickelberger proved that the discriminant of a number field is congruent to 0 or 1 modulo 4. We generalize this to an arbitrary (not necessarily commutative) ring of finite rank o…
A Norm Functor for Quadratic Algebras
Owen Biesel
Given commutative, unital rings and with a ring homomorphism making free of finite rank as an -module, we can ask for a "trace" or "norm" homomorphism takin…
A principle for converting Lindström-type lemmas to Stembridge-type theorems, with applications to walks, groves, and alternating flows
Owen Biesel
We prove that Fomin's generalization of Lindström's lemma for paths on acyclic directed graphs to walks on general directed graphs also generalizes a theorem of Stembridge in the s…
Isomorphisms of Discriminant Algebras
Owen Biesel, Alberto Gioia
For each natural number , we define a category whose objects are discriminant algebras in rank , i.e. functorial means of attaching to each rank- algebra a quadratic algeb…
Fine compactified moduli of enriched structures on stable curves
Owen Biesel, David Holmes
Enriched structures on stable curves over fields were defined by Maino in the late 1990s, and have played an important role in the study of limit linear series and degenerating jac…
Galois closure data for extensions of rings
Owen Biesel
To generalize the notion of Galois closure for separable field extensions, we devise a notion of -closure for algebras of commutative rings , where is locally free o…
A new discriminant algebra construction
Owen Biesel, Alberto Gioia
A discriminant algebra operation sends a commutative ring and an -algebra of rank to an -algebra of rank with the same discriminant bilinear form. C…
Néron models and the height jump divisor
Owen Biesel, David Holmes, Robin de Jong
We define an algebraic analogue, in the case of jacobians of curves, of the height jump divisor introduced recently by R. Hain. We give explicit combinatorial formulae for the heig…