arising from the localization sequence in algebraic K-theory has a torsion cokernel. Here p runs over a set of primes which satisfy a certain condition explained below. When C is an elliptic curve, all but finite number of primes p satisfy the condition. By using this fact, Langer and Saito give a finiteness result for the torsion subgroup of the Chow group CH(C × C)([LS]). When g = genus(C) > ...

Exact sequences are a well known notion in homological algebra. We investigate here the more vague properties of “homotopical exactness”, appearing for instance in the fibre or cofibre sequence of a map. Such notions of exactness can be given for very general “categories with homotopies” having homotopy kernels and cokernels, but become more interesting under suitable “stability” hypotheses, sa...

For a random matrix of entries sampled independently from fairly general distribution in $${{\mathbf {Z}}}$$ we study the probability that cokernel is isomorphic to given finite abelian group, or when it cyclic. This includes linear map between integer lattices by surjective. We show these statistics are asymptotically universal (as size goes infinity), precise formulas involving zeta values, a...

We prove that the integral Hurewicz image of the cokernel J spectrum detects precisely the Kervaire invariant one elements and nothing else, which may be viewed as an analogue of the Curtis–Madsen conjecture on the unstable mod 2 Hurewicz image of Q0S.

Let p be an odd prime and let k be a field finitely generated over the finite field with p elements. For any K3 surface X over k we prove that the the cokernel of the natural map Br(k) → Br(X) is finite modulo the p-primary torsion subgroup.