Hélène Esnault

Lectures on vanishing theorems

1 Kodairas vanishing theorem, a general discussion.- 2 Logarithmic de Rham complexes.- 3 Integral parts of Q-divisors and coverings.- 4 Vanishing theorems, the formal set-up.- 5 Vanishing theorems for invertible sheaves.- 6 Differential forms and higher direct images.- 7 Some applications of vanishing theorems.- 8 Characteristic p methods: Lifting of schemes.- 9 The Frobenius and its liftings.- 10 The proof of Deligne and Illusie [12].- 11 Vanishing theorems in characteristic p.- 12 Deformation theory for cohomology groups.- 13 Generic vanishing theorems [26], [14].- Appendix: Hypercohomology and spectral sequences.- References.

On Motives associated to graph polynomials

The appearance of multiple zeta values in anomalous dimensions and β-functions of renormalizable quantum field theories has given evidence towards a motivic interpretation of these renormalization group functions. In this paper we start to hunt the motive, restricting our attention to a subclass of graphs in four dimensional scalar field theory which give scheme independent contributions to the above functions.

The Arason invariant and mod 2 algebraic cycles

Introduction 73 1. Review of the Arason invariant 75 2. The special Clifford group 76 3. K-cohomology of split reductive algebraic groups 78 4. K-cohomology of BG 86 5. GL(N) and Cliff(n, n) 92 6. Two invariants for Clifford bundles 95 7. Snaking a Bloch-Ogus differential 100 8. Proof of Theorem 1 101 9. Application to quadratic forms 102 Appendix A. Toral descent 104 Appendix B. The Rost invariant 108 Appendix C. An amusing example 113 Acknowledgements 116 References 116

Varieties over a finite field with trivial Chow group of 0-cycles have a rational point

Smooth projective varieties

Effective bounds for semipositive sheaves and for the height of points on curves over complex function fields

X

Chow groups of projective varieties of very small degree

over a finite field

The coniveau filtration and non-divisibility for algebraic cycles

k

On Nori’s Fundamental Group Scheme

with

ALGEBRAIC VERSUS TOPOLOGICAL ENTROPY FOR SURFACES OVER FINITE FIELDS

CH_0(X\otimes \bar{k(X)})=\mathbb Z

Simply connected projective manifolds in characteristic p >0 have no nontrivial stratified bundles

have a rational point, in particular Fano varieties. We also refer to this http URL where the last version, cleaned from some typos, should be published online.