We define a class of invariants, which we call homological invariants, for persistence modules over a finite poset. Informally, a homological invariant is one that respects some homological data and takes values in the free abelian group generated by a…
We prove Fermat’s Last Theorem over and for prime exponents in certain congruence classes modulo by using a combination of the modular method and Brauer–Manin obstructions explicitly given by quadratic reciprocity constraints. The reciprocity const…
We introduce interpolated multiple Hurwitz polylogs and interpolated multiple Hurwitz zeta values. In addition, we discuss the generating functions for the sum of the polylogs/zeta values of fixed weight, depth, and all heights. The functions are expre…
A semigroup S is said to be right pseudo-finite if the universal right congruence can be generated by a finite set , and there is a bound on the length of derivations for an arbitrary pair as a consequence of those in U. This article explores the exis…
Motivated by the desire to understand the geometry of the basic loci in the reduction of Shimura varieties, we study their “group-theoretic models”—generalized affine Deligne–Lusztig varieties—in cases where they have a particularly nice description. C…
This paper provides a convenient and practical method to compute the homology and intersection pairing of a branched double cover of the 4-ball.To projections of links in the 3-ball, and to projections of surfaces in the 4-ball into the boundary sphere…