Hilbert's Theorem 90 and algebraic spaces

Simple item page
dc.creatorSchroeer, Stefan
dc.date2001-10-22
dc.date.accessioned2026-07-07T04:44:01Z
dc.date.available2026-07-07T04:44:01Z
dc.descriptionIn modern form, Hilbert's Theorem 90 tells us that R^1f_*(G_m)=0, where f is the canonical map between the etale site and the Zariski site of a scheme X. I construct examples showing that the corresponding statement for algebraic spaces does not hold. The first example is a nonseparated smooth 1-dimensional bug-eyed cover in Kollar's sense. The second example is a nonnormal proper algebraic space obtained by identifying points on suitable nonprojective smooth proper schemes.
dc.description6 pages, to appear in J. Pure Appl. Algebra
dc.identifierhttps://arxiv.org/abs/math/0110243
dc.identifierhttp://arxiv.org/abs/math/0110243
dc.identifierJ. Pure Appl. Algebra 173 (2002), 339-345
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/62466
dc.subjectAlgebraic Geometry
dc.subject14A20, 14C22, 14F20
dc.titleHilbert's Theorem 90 and algebraic spaces
dc.typetext

Files

Collections

arXiv