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Algebraic number fields, Algebraic integers, Arithmetic Geometry, Elliptic Curves, Function fields, Local fields, Arithmetic groups, Automorphic forms, zeta functions, $L$-functions, Quadratic forms, Quaternion algebras, Homogenous forms, Class groups, Units, Galois theory, Group cohomology, Étale cohomology, Motives, Class field theory, Iwasawa theory, Modular curves, Shimura varieties, Jacobian varieties, Moduli spaces
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Is there any definition of $H^1$ in one dimensional Arakelov geometry
There is a definition of $h^{1}(\overline{D})$ by many people, and a definition of $H^{1}(\overline{D})$ by Alexrander Borisov using the notion of ghost spaces of the second kind. But neither is the s …