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143
MODULAR INDEX INVARIANTS OF MUMFORD CURVES
, 2011
"... Modular index invariants of Mumford curves We continue an investigation initiated by Consani–Marcolli of the relation between the algebraic geometry of padic Mumford curves and the noncommutative geometry of graph C∗algebras associated to the action of the uniformizing padic Schottky group on the ..."
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Modular index invariants of Mumford curves We continue an investigation initiated by Consani–Marcolli of the relation between the algebraic geometry of padic Mumford curves and the noncommutative geometry of graph C∗algebras associated to the action of the uniformizing padic Schottky group
MODULAR INDEX INVARIANTS OF MUMFORD CURVES
, 2009
"... We continue an investigation initiated by Consani–Marcolli of the relation between the algebraic geometry of padic Mumford curves and the noncommutative geometry of graph C ∗algebras associated to the action of the uniformizing padic Schottky group on the Bruhat–Tits tree. We reconstruct invarian ..."
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invariants of Mumford curves related to valuations of generators of the associated Schottky group, by developing a graphical theory for KMS weights on the associated graph C ∗algebra, and using modular index theory for KMS weights. We give explicit examples of the construction of graph weights for low genus
Interaction and modular invariance of strings on curved manifolds
 Proceedings of the 16th Johns Hopkins Workshop, Curent Problems in Particle Theory (Goteborg
, 1992
"... We review and present new results for a string moving on an SU(1,1) group manifold. We discuss two classes of theories which use discrete representations. For these theories the representations forbidden by unitarity decouple and, in addition, one can construct modular invariant partition functions. ..."
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Cited by 13 (2 self)
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We review and present new results for a string moving on an SU(1,1) group manifold. We discuss two classes of theories which use discrete representations. For these theories the representations forbidden by unitarity decouple and, in addition, one can construct modular invariant partition functions
Modular Invariance and the Odderon
, 2008
"... We identify a new symmetry for the equations governing odderon amplitudes, corresponding in the Regge limit of QCD to the exchange of 3 reggeized gluons. The symmetry is a modular invariance with respect to the unique normal subgroup of SL(2, Z) of index 2. This leads to a natural description of the ..."
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We identify a new symmetry for the equations governing odderon amplitudes, corresponding in the Regge limit of QCD to the exchange of 3 reggeized gluons. The symmetry is a modular invariance with respect to the unique normal subgroup of SL(2, Z) of index 2. This leads to a natural description
1 Modular curves
"... We make some brief remarks on the relation of the mixmaster universe model of chaotic cosmology to the geometry of modular curves and to noncommutative geometry. We show that the full dynamics of the mixmaster universe is equivalent to the geodesic
ow on the modular curve X 0 (2). We then conside ..."
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We make some brief remarks on the relation of the mixmaster universe model of chaotic cosmology to the geometry of modular curves and to noncommutative geometry. We show that the full dynamics of the mixmaster universe is equivalent to the geodesic
ow on the modular curve X 0 (2). We then con
Linvariants of Tate Curves
"... Dedicated to Professor John Tate on the occasion of his eightieth birthday. Abstract: We compute the Greenberg’s Linvariant of the adjoint square of a Hilbert modular Galois representation, assuming a conjecture on the exact form of a certain universal Galois deformation ring (which is known to be ..."
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Dedicated to Professor John Tate on the occasion of his eightieth birthday. Abstract: We compute the Greenberg’s Linvariant of the adjoint square of a Hilbert modular Galois representation, assuming a conjecture on the exact form of a certain universal Galois deformation ring (which is known
The Odderon and Invariants of Elliptic Curves. ∗
, 1996
"... In this talk we present some links of the theory of the odderon with elliptic curves. These results were obtained in an earlier work [19]. The natural degrees of freedom of the odderon turn out to coincide with conformal invariants of elliptic curves with a fixed ‘sign’. This leads to a formulation ..."
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In this talk we present some links of the theory of the odderon with elliptic curves. These results were obtained in an earlier work [19]. The natural degrees of freedom of the odderon turn out to coincide with conformal invariants of elliptic curves with a fixed ‘sign’. This leads to a formulation
ON ANTICYCLOTOMIC µINVARIANTS OF MODULAR FORMS
"... Let E/Q be an elliptic curve of squarefree level N. Fix a prime p ≥ 5 of good reduction and an imaginary quadratic field K of discriminant prime to pN. Write N = N + N − with N + divisible only by primes which are split in K/Q and N − divisible only by inert primes. If N − has an even number of prim ..."
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Let E/Q be an elliptic curve of squarefree level N. Fix a prime p ≥ 5 of good reduction and an imaginary quadratic field K of discriminant prime to pN. Write N = N + N − with N + divisible only by primes which are split in K/Q and N − divisible only by inert primes. If N − has an even number
Special points on products of modular curves
, 2003
"... We prove the André–Oort conjecture on special points of Shimura varieties for arbitrary products of modular curves, assuming the Generalized Riemann Hypothesis. More explicitly, this means the following. Let n ≥ 0, and let Σ be a subset of C n consisting of points all of whose coordinates are jin ..."
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We prove the André–Oort conjecture on special points of Shimura varieties for arbitrary products of modular curves, assuming the Generalized Riemann Hypothesis. More explicitly, this means the following. Let n ≥ 0, and let Σ be a subset of C n consisting of points all of whose coordinates are jinvariants
Runge’s Method and Modular Curves
, 2009
"... We bound the jinvariant of Sintegral points on arbitrary modular curves over arbitrary fields, in terms of the congruence group defining the curve, assuming a certain Runge condition is satisfied by our objects. We then apply our bounds to prove that for sufficiently large prime p, the points of X ..."
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We bound the jinvariant of Sintegral points on arbitrary modular curves over arbitrary fields, in terms of the congruence group defining the curve, assuming a certain Runge condition is satisfied by our objects. We then apply our bounds to prove that for sufficiently large prime p, the points
Results 1  10
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143