RT Journal Article
T1 Moduli spaces for principal bundles in large characteristic
A1 Gómez Tomás, L.
A1 Langer, Adrián
A1 Schmitt, Alexander H.W.
A1 Sols, Ignacio
A2 Biswas, Indranil
A2 Kulkarni, Ravi S.
A2 Mitra, Sudeb
AB This paper  addresses the problem  of constructing  and compactifying moduli spaces of stable principal G  -bundles over smooth projective schemes for an arbitrary reductive group G  in both zero and nonzero characteristic. This involves  refining  the methods  of the  third  author [Transform. Groups 9 (2004), no. 2, 167–209; Int. Math. Res. Not. 2004, no. 62, 3327–3366;] and creating a unified formulation of the results of these papers and a paper of the first and fourth authors [Ann. of Math. (2) 161 (2005), no. 2, 1037–1092;]. The paper also complements a previous article by all four authors [Adv. Math. 219 (2008), no. 4, 1177–1245].  Particular features of the paper are the inclusion of  non-semisimple  groups and  non-faithful representations of G , a new approach to obtaining the semistable reduction theorem in characteristic zero and in large positive characteristic and a construction of the moduli space of decorated sheaves over projective varieties in arbitrary characteristic. The first main theorem states that, in characteristic zero and in large positive characteristic, coarse moduli spaces for (semi)stable singular principal G  -bundles can be defined using faithful representations (under some conditions) and exist as projective schemes. This covers many known cases, for example when G  is semisimple, for G=GL(V) , also for G  one of the classical groups O r (k) , SO r (k)  and Sp r (k)  provided the characteristic is not 2  and for groups of adjoint type.  In order  to use a  non-faithful representation ρ , singular principal G  -bundles must be replaced by principal ρ  -sheaves. The second main theorem states that the corresponding coarse moduli spaces exist as quasi-projective schemes  provided the base scheme is  a curve or the characteristic is zero. Both types of moduli space can be considered as compactifications of the moduli space of slope-stable rational  principal  G  -bundles.
PB Elsevier
SN 0001-8708, ESSN: 1090-2082
YR 2008
FD 2008
LK https://hdl.handle.net/20.500.14352/50555
UL https://hdl.handle.net/20.500.14352/50555
LA eng
DS Docta Complutense
RD 6 may 2024