Geodesic
Bounding Selmer Groups for the Rankin–Selberg Convolution of Coleman Families
Canadian journal of mathematics, Tome 73 (2021) no. 3, pp. 805-853

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DOI

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 $L_p$.
DOI : 10.4153/S0008414X2000019X
Mots-clés : Euler systems, Selmer complexes, Coleman families, p-adic L-functions, Galois representations 
Graham, Andrew; Gulotta, Daniel R.; Xu, Yujie. Bounding Selmer Groups for the Rankin–Selberg Convolution of Coleman Families. Canadian journal of mathematics, Tome 73 (2021) no. 3, pp. 805-853. doi: 10.4153/S0008414X2000019X
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     title = {Bounding {Selmer} {Groups} for the {Rankin{\textendash}Selberg} {Convolution} of {Coleman} {Families}},
     journal = {Canadian journal of mathematics},
     pages = {805--853},
     year = {2021},
     volume = {73},
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     doi = {10.4153/S0008414X2000019X},
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