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Jumps and Motivic Invariants of Semiabelian Jacobians
- Source :
- International Mathematics Research Notices. 2019:6437-6479
- Publication Year :
- 2018
- Publisher :
- Oxford University Press (OUP), 2018.
-
Abstract
- We investigate N\'eron models of Jacobians of singular curves over strictly Henselian discretely valued fields, and their behaviour under tame base change. For a semiabelian variety, this behaviour is governed by a finite sequence of (a priori) real numbers between 0 and 1, called "jumps". The jumps are conjectured to be rational, which is known in some cases. The purpose of this paper is to prove this conjecture in the case where the semiabelian variety is the Jacobian of a geometrically integral curve with a push-out singularity. Along the way, we prove the conjecture for algebraic tori which are induced along finite separable extensions, and generalize Raynaud's description of the identity component of the N\'eron model of the Jacobian of a smooth curve (in terms of the Picard functor of a proper, flat, and regular model) to our situation. The main technical result of this paper is that the exact sequence which decomposes the Jacobian of one of our singular curves into its toric and Abelian parts extends to an exact sequence of N\'eron models. Previously, only split semiabelian varieties were known to have this property.<br />Comment: 37 pages. Corrected two minor inaccuracies (added a factor of 1/[K':K] in the definition of Chai's base change conductor, and added the condition "purely wild" in Theorem 2.11)
- Subjects :
- Pure mathematics
Exact sequence
Mathematics - Number Theory
General Mathematics
010102 general mathematics
01 natural sciences
0101 Pure Mathematics
Separable space
Integral curve
Mathematics::Algebraic Geometry
Singularity
FOS: Mathematics
Number Theory (math.NT)
Identity component
0101 mathematics
Variety (universal algebra)
Algebraic number
Abelian group
Mathematics
Subjects
Details
- ISSN :
- 16870247 and 10737928
- Volume :
- 2019
- Database :
- OpenAIRE
- Journal :
- International Mathematics Research Notices
- Accession number :
- edsair.doi.dedup.....201f2ad86f65001f51ba6e43c4528837