Titlebook: Néron Models and Base Change; Lars Halvard Halle,Johannes Nicaise Book 2016 Springer International Publishing Switzerland 2016 14K15, 14H4

Aggressive

theta-waves

The Base Change Conductor and the Artin ConductorIn this chapter, we assume that . is algebraically closed. We will compare the base change conductor of the Jacobian variety of a .-curve . to the Artin conductor of . and other invariants of the curve, assuming that the genus of . is 1 or 2.

Conserve

Motivic Zeta Functions of Semi-Abelian VarietiesIn this chapter, we assume that . is algebraically closed. We will prove in Theorem 8.3.1.2 the rationality of the motivic zeta function of a Jacobian variety, and we show that it has a unique pole, which coincides with the tame base change conductor from Chap.?6 We will also investigate the case of Prym varieties.

Uncultured

Some Open ProblemsTo conclude, we will formulate some open problems and directions for future research stemming from the results in the preceding chapters. We assume that . is algebraically closed.

OUTRE

temperate

Néron Models and Base Change978-3-319-26638-1Series ISSN 0075-8434 Series E-ISSN 1617-9692

焦慮

甜瓜

燈絲

The Base Change Conductor and Edixhoven’s Filtration of this section states that the jumps of the Jacobian variety of a .-curve . only depend on the combinatorial reduction data of . (Theorem?6.3.1.3). This generalizes a previous result of the first author, where an additional condition on the reduction data was imposed.

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