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Global geometrised Rankin-Selberg method for GL(n)
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Global geometrised Rankin-Selberg method for GL(n)
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We propose a geometric interpretation of the classical Rankin-Selberg method for GL(n) in the framework of the geometric Langlands program. We show that the geometric Langlands conjecture for an irreducible unramified local system $E$ of rank $n$ on a curve implies the existence of automorphic sheaves corresponding to the universal deformation of $E$. Then we calculate the `scalar product' of two automorphic sheaves attached to this universal deformation.
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Cited by 1 Pith paper
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Diagonal cycles on Shtukas and the adjoint $L$-function
For split almost simple groups over function fields, self-intersections of diagonal cycles on shtuka moduli, with determinant line-bundle insertions, equal higher derivatives of adjoint L-functions.
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