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After preliminary definitions and a review (in the first section) of the basic structures (such as Frobenius Fm and Verschiebung Vm) of the Witt ring W(R) of a ring R, we present our main...
Already in the 1960s Grothendieck understood that one could obtain an almost entirely satisfactory theory of motives over a finite field when one assumes the Tate conjecture. In this not...
The ring of projective invariants of eight ordered points on the line is a quotient of the polynomial ring on V , where V is a fourteen-dimensional representation of S8, by an ideal I8, so the modular...
Consider the projective coordinate ring of the GIT quotient (P1)n//SL(2), with the usual linearization, where n is even. In 1894, Kempe proved that this ring is generated in degree one. In [HMSV2]we s...
The ring of projective invariants of n ordered points on the projective line is one of the most basic and earliest studied examples in Geometric Invariant Theory. It is a remarkable fact and the point...
The ring of projective invariants of n ordered points on the projective line is one of the most basic and earliest studied examples in Geometric Invariant Theory. It is a remarkable fact and the poin...
The moduli space of curves has proven itself a central object in geometry. The past decade has seen substantial progress in understanding the moduli space of curves, involving ideas, for example, fro...
First, we study a descending filtration of the ring of Fricke characters of a free group consisting of ideals on which the automorphism group of a free group acts. Then using it, we define a descendin...
We reinterpret and generalize conjectures of Lam and Williams as statements about the stationary distribution of a multispecies exclusion process on the ring. The central objects in our study are the ...
Using Galois cohomology, Schmoyer characterizes cryptographic non-trivial self-pairings of the $\ell$-Tate pairing in terms of the action of the Frobenius on the $\ell$-torsion of the Jacobian of a ge...
We consider the derived category of a specific non-Noetherian ring \Lambda, and show that there are objects in D(\Lambda) that are not Bousfield equivalent to any module. This answers a question posed...
We show that the complement of the ring of integers in a number field K is Diophantine. This means the set of ring of integers in K can be written as {t in K | for all x_1, ..., x_N in K, f(t,x_1, ......
Abstract: Let C be a Gorenstein curve which is either reduced or contained in a smooth algebraic surface. We show that the canonical ring R(C, \omega_C)=\oplus_{k \geq 0} H^0(C, \omega_C^k) is generat...
Abstract: For any graded commutative noetherian ring, where the grading group is abelian and where commutativity is allowed to hold in a quite general sense, we establish an inclusion-preserving bijec...

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