Berkovich log discrepancies in positive characteristic

On the Log Discrepancies in Mori Contractions

It was conjectured by McKernan and Shokurov that for all Mori contractions from X to Y of given dimensions, for any positive ε there is a positive δ such that if X is ε-log terminal, then Y is δ-log terminal. We prove this conjecture in the toric case and discuss the dependence of δ on ε, which seems mysterious.

Canon-log Transfer Characteristic

In Positive Characteristic

We establish Noether’s inequality for surfaces of general type in positive characteristic. Then we extend Enriques’ and Horikawa’s classification of surfaces on the Noether line, the so-called Horikawa surfaces. We construct examples for all possible numerical invariants and in arbitrary characteristic, where we need foliations and deformation techniques to handle characteristic 2. Finally, we ...

Transcendence in Positive Characteristic

1. Table of symbols 2 2. Transcendence for Drinfeld modules 2 2.1. Wade’s results 2 2.2. Drinfeld modules 3 2.3. The Weierstraß-Drinfeld correspondence 3 2.4. Carlitz 5 2.5. Yu’s work 6 3. t-Modules 7 3.1. Definitions 7 3.2. Yu’s sub-t-module theorem 8 3.3. Yu’s version of Baker’s theorem 8 3.4. Proof of Baker-Yu 8 3.5. Quasi-periodic functions 9 3.6. Derivatives and linear independence 12 3.7....

Nilpotent Orbits in Positive Characteristic

Let G be a connected reductive linear algebraic group defined over an algebraically closed field of characteristic p. Assume that p is good for G. In this note we classify all the spherical nilpotent G-orbits in the Lie algebra of G. The classification is the same as in the characteristic zero case obtained by D.I. Panyushev in 1994, [32]: for e a nilpotent element in the Lie algebra of G, the ...