Let f and g be two cuspidal modular forms and let ${\mathcal {F}}$ be a Coleman family passing through f, defined over an open affinoid subdomain V of weight space $\mathcal {W}$ . Using ideas of Pottharst, under certain hypotheses on f and $g,$ we construct a coherent sheaf over $V \times \mathcal {W}$ that interpolates the Bloch–Kato Selmer group of the Rankin–Selberg convolution of two modular forms in the critical range (i.e, the range where the p-adic L-function $L_p$ interpolates critical values of the global L-function). We show that the support of this sheaf is contained in the vanishing locus of $L_p$ .

令f和g是两个尖点模形式，并令 ${\mathcal {F}}$ 是通过f的 Coleman 族，定义在权重空间 $\mathcal {W}$ 的开放类同子域V上。使用 Pottharst 的思想，在f和 $g 的某些假设下， 我们在 $V \times \mathcal {W}$ 上构建了一个相干层，它插入了两个模形式的 Rankin-Selberg 卷积的 Bloch-Kato Selmer 群临界范围（即，范围在p进制大号-function $ $ L_P 内插全局L函数的临界值）。我们表明该层的支持包含在 $L_p$ 的消失轨迹中。