144 research outputs found
Moduli of formal torsors
We construct the moduli stack of torsors over the formal punctured disk in
characteristic p > 0 for a finite group isomorphic to the semidirect product of
a p-group and a tame cyclic group. We prove that the stack is a limit of
separated Deligne-Mumford stacks with finite and universally injective
transition maps.Comment: 37 pages, some improvements to the main resul
ACM bundles on del Pezzo surfaces
ACM rank 1 bundles on del Pezzo surfaces are classified in terms of the
rational normal curves that they contain. A complete list of ACM line bundles
is provided. Moreover, for any del Pezzo surface of degree less or equal
than six and for any we construct a family of dimension of
non-isomorphic simple ACM bundles of rank on
Stacks of uniform cyclic covers of curves and their Picard groups
We study the stack B_{h,g,n} of uniform cyclic covers of degree n between
smooth curves of genus h and g and, for h >> g, present it as an open substack
of a vector bundle over the universal Jacobian stack of M_g. We use this
description to compute the integral Picard group of B_{h,g,n}, showing that it
is generated by tautological classes of B_{h,g,n}.Comment: v3: (long overdue) final versio
Ramified Galois covers via monoidal functors
We interpret Galois covers in terms of particular monoidal functors,
extending the correspondence between torsors and fiber functors. As
applications we characterize tame -covers between normal varieties for
finite and \'etale group schemes and we prove that, if is a finite, flat
and finitely presented nonabelian and linearly reductive group scheme over a
ring, then the moduli stack of -covers is reducible.Comment: 20 page
Trace map and regularity of finite extensions of a DVR
We interpret the regularity of a finite and flat extension of a discrete
valuation ring in terms of the trace map of the extension.Comment: 9 pages, final versio
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