Let X --> P^1 be a Z/n-branched cover over a complete discretely valued field K, where n does not divide the residue characteristic of K. We explicitly construct the minimal regular normal crossings model of X over the valuation ring of K. By “explicitly”, we mean that we construct a normal model of P^1 whose normalization in K(X) is the desired regular model. The normal model of P^1 is fully encoded as a basket of finitely many discrete valuations on the rational function field K(P^1), each of which is given using Mac Lane’s 1936 notation involving finitely many polynomials and rational numbers. This is joint work with Padmavathi Srinivasan.
Algebra Seminar
Monday, March 31, 2025 - 3:30pm
Andrew Obus
CUNY
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