Let A be a complete discrete valuation ring with possibly imperfect residue field, and let χ be a one-dimensional Galois representation over A. I show that the non-logarithmic variant of Kato’s Swan conductor is the same for χ and the pullback of χ to the generic residual perfection of A. This implies the conductor from “Conductors and the moduli of residual perfection” [4] extends the non-loga...

Building on the work of K. Chiba (J. Algebra 263 (2003), 75– 87), we present sufficient conditions for the completion of a division ring with respect to the metric defined by a discrete valuation function to contain a free field, i.e. the universal field of fractions of a free associative algebra. Several applications to division rings generated by torsion-free nilpotent groups, skew Laurent se...

Suppose O is a complete discrete valuation ring of positive characteristic with perfect residue field. The category of finite flat strict modules was recently introduced by Faltings and appears as an equal characteristic analogue of the classical category of finite flat group schemes. In this paper we obtain a classification of these modules and apply it to prove analogues of properties, which ...

We study the problem of when the collection of the recession cones of a polyhedral complex forms also a complex. We exhibit an example showing that this is no always the case. We also show that if the support of the given polyhedral complex satisfies a Minkowski-Weyl type condition, then the answer is positive. As a consequence, we obtain a classification theorem for proper toric schemes over a...

In analogy with the notion of the composite semi-valuations, we deene the composite G-valuation v from two other G-valuations w and u. We consider a lexicographically exact sequence (a;) : Au ! Bv ! Cw and the composite G-valuation v of a eld K with value group Bv. If the assigned to v set Rv = fx 2 K=v(x) 0 or v(x) non comparable to 0g is a local ring, then a G-valuation w of K into Cw is deen...

Let O be a complete discrete valuation ring, K its quotient field, and A the symmetric Kronecker algebra over O. We consider full subcategory of category A-lattices whose objects are M such that M⊗OK is projective A⊗OK-modules. In this paper, we study Heller lattices indecomposable periodic modules A. As main result, determine shapes stable Auslander–Reiten components containing

where t is induced by the tame symbols on R. They have also asked whether this sequence remains exact with "0 -•" inserted on the left when R is a ring of algebraic integers. In this note we announce an affirmative response when R is a discrete valuation ring, and a proof that the resulting sequence is split exact under certain additional hypotheses on R. In addition, we derive consequences of ...

for 1 ≤ i ≤ m. Suppose that P ⊂ R is a regular prime (R/P is a regular local ring) and 0 6= f ∈ P . The regular local ring R1 = R[ P f ]m where m is a maximal ideal of R[ P f ] containing mR is called a monoidal transform of R. Suppose that V is a valuation ring of the quotient field of S which dominates S (and thus dominates R). Then given a regular prime P of R (or of S) there exists a unique...

Let R be a complete discrete valuation ring of mixed characteristic (0, p) with fraction field K. We study stable models of p-cyclic covers of PK . First, we determine the monodromy extension, the monodromy group, its filtration and the Swan conductor for special covers of arbitrarily high genus with potential good reduction. In the case p = 2 we consider hyperelliptic curves of genus 2.

It is shown that if K is an algebraically closed valued eld with valuation ring R, then Th(K) has elimination of imaginaries if sorts are added whose elements are certain cosets in K n of certain deenable R-submodules of K n (for all n 1). The proof involves the development of a theory of independence for unary types, which play the role of 1-types, followed by an analysis of germs of deenable ...