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This article concerns solutions to the anti-self-dual Yang Mills (ASDYM) equations in split signature that are global on the double cover of the appropriate conformally compactified Minkowski space = S 2 × S 2 . Ward's ASDYM twistor construction is adapted to this geometry using a correspondence...
It is shown that if K is an algebraically closed valued field with valuation ring R , then Th( K ) has elimination of imaginaries if sorts are added whose elements are certain cosets in K n of certain definable R -submodules of K n (for all ). The proof involves the development of a theory of...
We use arithmetic models of modular curves to establish some properties of Ramanujan's continued fraction. In particular, we give a new geometric proof that its singular values are algebraic units that generate specific abelian extensions of imaginary quadratic fields, and we use a mixture of...
We construct canonical heights of subvarieties for dynamical eigensystems of several morphisms for line bundles over a number field, and study some of their properties. We also construct invariant currents for such systems over ℂ.
If E is an elliptic curve over ℚ and K is an imaginary quadratic field, there is an Iwasawa main conjecture predicting the behavior of the Selmer group of E over the anticyclotomic ℤ p -extension of K . The main conjecture takes different forms depending on the sign of the functional equation...
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