42 citations · 137 across the 25 of their papers we have counts for
29 papers
A relative orientation for the moduli space of stable maps to a del Pezzo surface
Jesse Leo Kass, Marc Levine, Jake P. Solomon +1
We prove orientation results for evaluation maps of moduli spaces of rational stable maps to del Pezzo surfaces over a field, both in characteristic and in positive characteris…
A quadratically enriched count of rational curves
Jesse Leo Kass, Marc Levine, Jake P. Solomon +1
We define a quadratically enriched count of rational curves in a given divisor class passing through a collection of points on a del Pezzo surface of degree over a per…
Quadratic enrichment of the logarithmic derivative of the zeta function
Margaret Bilu, Wei Ho, Padmavathi Srinivasan +2
We define an enrichment of the logarithmic derivative of the zeta function of a variety over a finite field to a power series with coefficients in the Grothendieck--Witt group. We…
On quadratically enriched excess and residual intersections
Tom Bachmann, Kirsten Wickelgren
We use recent duality results of Eisenbud--Ulrich to give tools to study quadratically enriched residual intersections when there is no excess bundle. We use this to prove a formul…
An explicit self-duality
Nikolas Kuhn, Devlin Mallory, Vaidehee Thatte +1
We provide an exposition of the canonical self-duality associated to a presentation of a finite, flat, complete intersection over a Noetherian ring, following work of Scheja and St…
Applications to A1-enumerative geometry of the A1-degree
Sabrina Pauli, Kirsten Wickelgren
These are lecture notes from the conference Arithmetic Topology at the Pacific Institute of Mathematical Sciences on applications of Morel's A1-degree to questions in enumerative g…
A^1-Euler classes: six functors formalisms, dualities, integrality and linear subspaces of complete intersections
Tom Bachmann, Kirsten Wickelgren
We equate various Euler classes of algebraic vector bundles, including those of [BM, KW, DJK], and one suggested by M.J. Hopkins, A. Raksit, and J.-P. Serre. We establish integrali…
Unstable Motivic Homotopy Theory
Kirsten Wickelgren, Ben Williams
We give an introduction to unstable motivic homotopy theory of Morel and Voevodsky, and survey some results.
An Example of Wild Ramification in an Enriched Riemann-Hurwitz Formula
Candace Bethea, Jesse Leo Kass, Kirsten Wickelgren
M. Levine proved an enrichment of the classical Riemann-Hurwitz formula to an equality in the Grothendieck-Witt group of quadratic forms. In its strongest form, Levine's theorem in…
An arithmetic count of the lines meeting four lines in P^3
Padmavathi Srinivasan, Kirsten Wickelgren
We enrich the classical count that there are two complex lines meeting four lines in space to an equality of isomorphism classes of bilinear forms. For any field , this enrichme…
The Galois action on the lower central series of the fundamental group of the Fermat curve
Rachel Davis, Rachel Pries, Kirsten Wickelgren
Information about the absolute Galois group of a number field is encoded in how it acts on the étale fundamental group of a curve defined over . In the case th…
An étale realization which does not exist
Jesse Leo Kass, Kirsten Wickelgren
For a global field, local field, or finite field with infinite Galois group, we show that there can not exist a functor from the Morel--Voevodsky -homotopy catego…
An Arithmetic Count of the Lines on a Smooth Cubic Surface
Jesse Leo Kass, Kirsten Wickelgren
We give an arithmetic count of the lines on a smooth cubic surface over an arbitrary field , generalizing the counts that over there are lines, and over $\math…
The Galois action and cohomology of a relative homology group of Fermat Curves
Rachel Davis, Rachel Pries, Vesna Stojanoska +1
For an odd prime satisfying Vandiver's conjecture, we give explicit formulae for the action of the absolute Galois group on the homology of the degree …
The class of Eisenbud--Khimshiashvili--Levine is the local A1-Brouwer degree
Jesse Leo Kass, Kirsten Wickelgren
Given a polynomial function with an isolated zero at the origin, we prove that the local A1-Brouwer degree equals the Eisenbud-Khimshiashvili-Levine class. This answers a question…
A classical proof that the algebraic homotopy class of a rational function is the residue pairing
Jesse Leo Kass, Kirsten Wickelgren
Cazanave has identified the algebraic homotopy class of a rational function of variable with an explicit nondegenerate symmetric bilinear form. Here we show that Hurwitz's proo…
Massey products <y,x,x,...,x,x,y> in Galois cohomology via rational points
Kirsten Wickelgren
For an element of a field other than or , we compute the order Massey products of factors of…
The simplicial suspension sequence in A^1-homotopy
Aravind Asok, Kirsten Wickelgren, Ben Williams
We study a version of the James model for the loop space of a suspension in unstable -homotopy theory. We use this model to establish an analog of G.W. Whitehead's c…
Desuspensions of S^1 /\ P^1_Q-{0,1,infty}
Kirsten Wickelgren
We use the Galois action on to show that the homotopy equivalence $S^1 \wedge (\mathbb{G}_{m,\mathbb{Q}}…
The Simplicial EHP Sequence in A1-Algebraic Topology
Kirsten Wickelgren, Ben Williams
We give a tool for understanding simplicial desuspension in A1-algebraic topology: we show that is a fiber sequence up to homoto…
Galois action on the homology of Fermat curves
Rachel Davis, Rachel Pries, Vesna Stojanoska +1
In his paper titled "Torsion points on Fermat Jacobians, roots of circular units and relative singular homology", Anderson determines the homology of the degree Fermat curve as…
Classification of problematic subgroups of U(n)
Julia E. Bergner, Ruth Joachimi, Kathryn Lesh +2
We classify p-toral subgroups of U(n) that can have non-contractible fixed points under the action of U(n) on the complex of partitions of complex n-space into mutually orthogonal…
Fixed points of -toral groups acting on partition complexes
Julia E. Bergner, Ruth Joachimi, Kathryn Lesh +2
We consider the action of -toral subgroups of on the unitary partition complex . We show that if is -toral and has noncontractible fixe…
An Abel map to the compactified Picard scheme realizes Poincaré duality
Jesse Leo Kass, Kirsten Wickelgren
For a smooth algebraic curve X over a field, applying H_1 to the Abel map X -> Pic (X/\partial X) to the Picard scheme of X modulo its boundary realizes the Poincaré duality isomor…