NERON MODELS AND THE HEIGHT JUMP DIVISOR

作者：Biesel Owen^*; Holmes David; De Jong Robin

来源：Transactions of the American Mathematical Society, 2017, 369(12): 8685-8723.

DOI：10.1090/tran/7087

• Canonical height
• Deligne pairing
• dual graph
• effective resistance
• Green's function
• height jump divisor
• labelled graph
• Neron model
• resistive network

We define an algebraic analogue, in the case of jacobians of curves, of the height jump divisor introduced recently by R. Hain. We give explicit combinatorial formulae for the height jump for families of semistable curves using labelled reduction graphs. With these techniques we prove a conjecture of Hain on the effectivity of the height jump, and also give a new proof of a theorem of Tate, Silverman and Green on the variation of heights in families of abelian varieties.

• 出版日期2017-12