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The intersection matrices of and some applications
Debargha Banerjee, Priyanka Majumder, Chitrabhanu Chaudhuri
We compute intersection matrices for modular curves of the form with and as an application, we compute an asymptotic expression for the Arakelov self-int…
The Heisenberg covering of the Fermat curve
Debargha Banerjee, Loïc Merel
For integer , K. Murty and D. Ramakrishnan defined the -th Heisenberg curve, as the compactified quotient of the upper half-plane by a certain non-congruence su…
Ordinary local representations and $\Ext$ groups
Debargha Banerjee, Srijan Das
We can associate an admissible unitary representation of $\GL_2(\Q_p)$ with every local Galois representation by the -adic local Langlands correspondence. If $ρ_p…
Towards a mod- Lubin-Tate theory for $\GL_2$ over totally real fields
Debargha Banerjee, Vivek Rai
We show that the conjectural mod local Langlands correspondence can be realised in the mod cohomology of the Lubin-Tate towers. The proof utilizes a well known conjecture o…
The Eisenstein cycles and Manin Drinfeld properties
Debargha Banerjee, Loic Merel
Consider a subgroup of finite index of modular group. We give an analytic criterion for a cuspidal divisor to be torsion in the Jacobian of the corresponding modular curve. By Bely…