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Algebraic Geometry, Arithmetic Geometry
"... 2004 4. Mochizuki’s indigenous bundles and Ehrhart polynomials, with Fu Liu. Journal of Algebraic Combinatorics, 23 (2006), no. 2, 125–136. 2004 5. Rational functions with given ramification in characteristic p. Compositio Mathematica, 142 (2006), no. 6, 433–450. 2004 6. A limit linear series moduli ..."
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2004 4. Mochizuki’s indigenous bundles and Ehrhart polynomials, with Fu Liu. Journal of Algebraic Combinatorics, 23 (2006), no. 2, 125–136. 2004 5. Rational functions with given ramification in characteristic p. Compositio Mathematica, 142 (2006), no. 6, 433–450. 2004 6. A limit linear series moduli scheme. Annales de l’Institut Fourier, 56 (2006), no. 4, 11651205. 2004 7. Logarithmic connections with vanishing pcurvature. Submitted for publication. 2004 8. Frobeniusunstable bundles and pcurvature. Transactions of the AMS, to appear. 2004 9. The generalized Verschiebung for curves of genus 2. Mathematische Annalen, 336 (2006), no. 4, 963986. 2004 10. Deformations of covers, BrillNoether theory, and wild ramification. Mathematical Research
Applications of Arithmetical Geometry to Cryptographic Constructions
 Proceedings of the Fifth International Conference on Finite Fields and Applications
"... Public key cryptosystems are very important tools for data transmission. Their performance and security depend on the underlying crypto primitives. In this paper we describe one such primitive: The Discrete Logarithm (DL) in cyclic groups of prime order (Section 1). To construct DLsystems we use me ..."
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Cited by 50 (1 self)
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methods from algebraic and arithmetic geometry and especially the theory of abelian varieties over finite fields. It is explained why Jacobian varieties of hyperelliptic curves of genus 4 are candidates for cryptographically "good" abelian varieties (Section 2). In the third section we describe
Modular forms and arithmetic geometry
, 2003
"... The aim of these notes is to describe some examples of modular forms whose Fourier coefficients involve quantities from arithmetical algebraic geometry. At the moment, no general theory of such forms exists, but the examples suggest that they should be viewed as a kind of arithmetic analogue of thet ..."
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The aim of these notes is to describe some examples of modular forms whose Fourier coefficients involve quantities from arithmetical algebraic geometry. At the moment, no general theory of such forms exists, but the examples suggest that they should be viewed as a kind of arithmetic analogue
Supergeometry and Arithmetic Geometry
 Nuclear Physics B, Volume 756, Issue
"... We define a superspace over a ring R as a functor on a subcategory of the category of supercommutative Ralgebras. As an application the notion of a padic superspace is introduced and used to give a transparent construction of the Frobenius map on padic cohomology of a smooth projective variety ov ..."
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over Zp (the ring of padic integers). 1 Superspaces The basic object of study in algebraic geometry is the solution set of a system of polynomial equations. Let us stress that you should really be looking at the solutions of your equations anywhere they make sense; this leads to the functorial
Derivatives of Eisenstein Series and Arithmetic Geometry
 ICM 2002 · VOL. III · 1–3
, 2002
"... We describe connections between the Fourier coefficients of derivatives of Eisenstein series and invariants from the arithmetic geometry of the Shimura varieties M associated to rational quadratic forms (V, Q) of signature (n,2). In the case n = 1, we define generating series ˆ φ1(τ) for 1cycles (r ..."
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Cited by 7 (0 self)
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We describe connections between the Fourier coefficients of derivatives of Eisenstein series and invariants from the arithmetic geometry of the Shimura varieties M associated to rational quadratic forms (V, Q) of signature (n,2). In the case n = 1, we define generating series ˆ φ1(τ) for 1cycles
On different notions of tameness in arithmetic geometry
, 2009
"... Abstract: The notion of a tamely ramified covering is canonical only for curves. Several notions of tameness for coverings of higher dimensional schemes have been used in the literature. We show that all these definitions are essentially equivalent. Furthermore, we prove finiteness theorems for the ..."
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Cited by 16 (4 self)
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for the tame fundamental groups of arithmetic schemes. 1
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