CONSERVATION THEOREMS ON SEMI-CLASSICAL ARITHMETIC

B + L Non - Conservation as a Semi - Classical Process ∗

I discuss the problem of computing B+L violation at high energies as that of solving classical differential equations. These equations involve boundary conditions at initial and a final times which are anti-Feynman, and involve solving non-linear differential equations which are complex, even if the original Hamiltonian was real. ∗Presented at the XXXIII Crakow School of Physics, Zakopane, Pola...

Classical arithmetic is part of intuitionistic arithmetic

One of Michael Dummett’s most striking contributions to the philosophy of mathematics is an argument to show that the correct logic to apply in mathematical reasoning is not classical but intuitionistic. In this article I wish to cast doubt on Dummett’s conclusion by outlining an alternative, motivated by consideration of a well-known result of Kurt Gödel, to the standard view of the relationsh...

Arithmetic and the Incompleteness Theorems

Arithmetic Duality Theorems Second Edition

Semi-stable extensions on arithmetic surfaces

Let S be a smooth projective curve over the complex numbers and X → S a semi-stable projective family of curves. Assume that both S and the generic fiber of X over S have genus at least two. Then the sheaf of absolute differentials ΩX defines a vector bundle on X which is semi-stable in the sense of Mumford-Nakano with respect to the canonical line bundle on X . The Bogomolov inequality c1(Ω 1 ...