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The motivic fundamental group of P1∖{0,1,∞} and the theorem of Siegel
In this paper, we establish a link between the structure theory of the pro-unipotent motivic fundamental group of the projective line minus three points and Diophantine geometry. In particular, weExpand
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The Spitzer Extragalactic Representative Volume Survey (SERVS): Survey Definition and Goals
We present the Spitzer Extragalactic Representative Volume Survey (SERVS), an 18 square degrees medium-deep survey at 3.6 and 4.5 microns with the post-cryogenic Spitzer Space Telescope to ~2 microJyExpand
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A p-adic nonabelian criterion for good reduction of curves
3 Universal unipotent objects 9 3.1 The Kummer etale site . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 3.2 The etale category . . . . . . . . . . . . . . . . . . . . . . . . . .Expand
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Heat-mapping: A robust approach toward perceptually consistent mesh segmentation
TLDR
We exploit the intelligence of the heat as a global structure-aware message on a meshed surface and develop a robust PCMS scheme, called Heat-Mapping based on the heat kernel. Expand
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Massey products for elliptic curves of rank 1
  • M. Kim
  • Mathematics
  • 29 January 2009
For an elliptic curve over Q of analytic rank 1, we use the level-two Selmer variety and secondary cohomology products to find explicit analytic defining equations for global integral points insideExpand
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p-adic L-functions and Selmer varieties associated to elliptic curves with complex multiplication
  • M. Kim
  • Mathematics
  • 28 October 2007
We show how the finiteness of integral points on an elliptic curve over Q with complex multiplication can be accounted for by the nonvanishing of L-functions that leads to bounds for dimensions ofExpand
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The unipotent Albanese map and Selmer varieties for curves
  • M. Kim
  • Mathematics
  • 20 October 2005
We study the unipotent Albanese map that associates the torsor of paths for p-adic fundamental groups to a point on a hyperbolic curve. It is shown that the map is very transcendental in nature,Expand
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PURELY INSEPARABLE POINTS ON CURVES OF HIGHER GENUS
has solution (t, 1) in K = k(t). Given any such f we can keep ‘twisting’ its coefficients with the Frobenius map of K and get new polynomials f (x, y) (by which we denote the nth twist) and newExpand
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Selmer varieties for curves with CM Jacobians
We study the Selmer variety associated to a canonical quotient of the $\Q_p$-pro-unipotent fundamental group of a smooth projective curve of genus at least two defined over $\Q$ whose JacobianExpand
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Learning Algebraic Structures: Preliminary Investigations
  • Y. He, M. Kim
  • Computer Science, Mathematics
  • ArXiv
  • 2 May 2019
TLDR
We employ techniques of machine-learning, exemplified by support vector machines and neural classifiers, to initiate the study of whether AI can "learn" algebraic structures. Expand
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