arXiv subjects
Publications and source records attributed to Shahram Biglari.
We reformulate a conjecture of Beauville on algebraic cycles on an abelian variety in terms of certain compatibility and vanishings of some naturally defined filtrations on the Grothendieck group of the abelian variety.
In this note we consider the coniveau filtration on the Grothendieck group of a regular separated noetherian scheme and its behavior with respect to the multiplication and the lambda ring structure. We show that a weak multiplicativity result can be proved. A strong compatibility result on Adams operations is also obtained.
The additivity of traces in certain tensor triangulated categories for endomorphisms of finite order of distinguished triangles is investigated. For the identity endomorphism this has been fully established by J. P. May ("The additivity of traces in triangulated categories", Adv. Math., 2001, 163, 34-73). By imposing extra conditions on the coefficients we show how May's result implies a stronger additivity.
In this note we show that similar to the classical case the ring of representations of symmetric groups in a tensor derived category is certain ring of symmetric functions. We also show that in the general setting considered here, the Adams operations compute the characteristic series associated to powers of endomorphisms.
We prove a few results concerning the notions of finite dimensionality of mixed Tate motives in the sense of Kimura and O'Sullivan. It is shown that being oddly or evenly finite dimensional is equivalent to vanishing of certain cohomology groups defined by means of Levine weight filtration. We then explain the relation to the Grothendieck group of the triangulated category D of mixed Tate motives. This naturally gives rise to a λ-ring structure on K_0(D).
Using a Zariski topology associated to a finite field extensions, we give new proofs and generalize the primitive and normal basis theorems.