specifically those of translation, reprinting, re-use of illustrations, broadcasting, reproduction by photocopying machine or similar means, and storage in data banks. Under Â§ 54 of the Germanâ€¦ (More)

Preface These notes are based on a course given at the Tata Institute of Fundamental Research in the beginning of 1990. The aim of the course was to describe the solution by O. Mathieu of someâ€¦ (More)

We classify the complex Laurent polynomials with the property that their powers have no constant term. The result confirms a conjecture of Mathieu for the case of tori. (A different case would implyâ€¦ (More)

Let the reductive group G act on the finitely generated commutative k-algebra A. We ask if the finite generation property of the ring of invariants extends to the full cohomology ring. We confirmâ€¦ (More)

It is known that the Grauert-Riemenschneider vanishing theorem is not valid in characteristic p ([1]). Here we show that it may be restored in the presence of a suitable Frobenius splitting. Theâ€¦ (More)

We exhibit a nice Frobenius splitting Ïƒ on GÃ— b where b is the Lie algebra of the Borel group B of upper triangular matrices in the general linear group G = Gln. What is nice about it, is that itâ€¦ (More)

Let R be a commutative noetherian d-dimensional ring. Recall that for n > d + 2 the group E,(R) (the subgroup of GL,(R) generated by elementary matrices) acts transitively on Urn,,(R), the set ofâ€¦ (More)

LetG be a reductive linear algebraic group over a field k. LetA be a finitely generated commutative k-algebra on which G acts rationally by k-algebra automorphisms. Invariant theory states that theâ€¦ (More)

Let B be the maximum of the entries of GG. The main issue is whether we can estimate the entries of b in terms of B, m, n during the algorithm. The entries of A can then be estimated through A = bG.â€¦ (More)

Let G = GLN or SLN as reductive linear algebraic group over a field k of characteristic p > 0. We prove several results that were previously established only when N â‰¤ 5 or p > 2 : Let G actâ€¦ (More)