Suppose a connected reductive complex algebraic group G acts linearly on a complex projective variety X. We prove that if 1→ N → G→ H → 1 is a short exact sequence of connected reductive groups and X the open set of semistable points for the action of N on X then IH H (X/N) is a direct summand of IH G (X). The inclusion is provided by the decomposition theorem and certain resolutions of the act...

Commodity loans are presented as an interpretation of spreads between spot and futures prices in commodity markets. This interpretation suggests an alternative to convenience yield as an explanation for the existence of large positive differences between spot and futures prices that are inconsistent with the usual arbitrage arguments. A model is presented in which an owner of a stock of a commo...

The purpose of this paper is to give a brief general account of the completely reducible finite-dimensional representations of a locally finite group G over a given algebraically closed field K. Theorem 1 shows that all such representations of G can be brought down to the algebraic closure F in K of the prime field of K. This reduces all further considerations in this account to countable group...

The structure of an algebraic tamely ramified extension of a henselian valued field is studied. We will prove, in theorem 3.2, the following statement: A finite extension L/K is tamely ramified if and only if the field L is obtained from the maximal unramified extension T by adjoining the radicals m √ t, with t ∈ T, m ∈ N, m ≥ 1, (m, p) = 1, where p is the characteristic of the residue class fi...

We introduce the tropical $F$-polynomial $f_M$ of a quiver representation $M$. study its interplay with general presentation for any finite-dimensional basic algebra. give an interpretation evaluating at weight vector. As consequence, we Newton polytope ${\sf N}(M)$ dual fan and 1-skeleton N}(M)$. propose algorithm to determine generic polytopes, show it works path algebras. application, repres...