In the classical paper [A-H] Adams-Hilton constructed a free chain algebra which is an important algebraic model of a simply connected homotopy type. We show that this chain algebra (endowed with an additional structure given by a “height function”) yields actually an invariant of a proper homotopy type. For this we introduce the homotopy category of locally finite chain algebras without using ...

Z N×N = {f : N× N → Z}). Then, several undecidability results are established, leading to a convenient data structure for effective machine computations. We call this data structure a locally effective matrix. We study when (and how) the standard matrix calculus (Ker and CoKer computations) can be extended to the infinite case. We find again several undecidability barriers. When these limitatio...

We show that if over some number field there exists a certain diagonal plane cubic curve that is locally solvable everywhere, but that does not have points over any cubic galois extension of the number field, then the algebraic part of the Brauer-Manin obstruction is not the only obstruction to the Hasse principle for K3 surfaces.

We prove vanishing results for Lie groups and algebraic groups (over any local field) in bounded cohomology. The main result is a vanishing below twice the rank for semi-simple groups. Related rigidity results are established for S-arithmetic groups and groups over global fields. We also establish vanishing and cohomological rigidity results for products of general locally compact groups and th...

It is known that any MV -algebra is a topological MV -algebra. For a locally finite MV -algebra A with some algebraic and topological conditions the product A× A becomes a compact Riemann surface (modulo conformal equivalence). Topologically, it is a torus.

Let G be a reductive algebraic group, with nilpotent cone N and flag variety B. We construct an exact functor from perverse sheaves on N to locally constant sheaves on B, and we use it to study Ext-groups and stalks of simple perverse sheaves on N in terms of the cohomology of B. 2010 Mathematics Subject Classification: Primary 20G05; Secondary 14F05, 32S60.

Recently N. Nitsure showed that for a coherent sheaf F on a noetherian scheme the automorphism functor AutF is representable if and only if F is locally free. Here we remove the noetherian hypothesis and show that the same result holds for the endomorphism functor EndF even if one asks for representability by an algebraic space.

Algebraic varieties that are locally isomorphic to open subsets of affine space will be called plain. Plain varieties are smooth and rational. The converse is true for curves and surfaces, and is unknown in general. It is shown that plain varieties are stable under blowup in smooth centers.

Every three-dimensional complex algebraic variety with isolated singular point has a resolution factoring through the Nash blowup and the blowup of the maximal ideal over which the second Fitting ideal sheaf is locally principal. In such resolutions one can construct Hsiang-Pati coordinates and thus obtain generators for the Nash sheaf that are the differentials of monomial functions.

Admissible locally-free sheaves on P, also known in the literature as mathematical instanton bundles, arise in twistor theory, and are in 1-1 correspondence with instantons on R. In this paper, we study admissible sheaves on P from the algebraic geometric point of view. We discuss examples and compare the admissibility condition with semistability and splitting type.