Motivated by the conjectures of “Mazur-Tate-Teitelbaum type” formulated in [BD1] and by the main result of [BD3], we describe a conjectural construction of a global point PK ∈ E(K), where E is a (modular) elliptic curve over Q of prime conductor p, and K is a real quadratic field satisfying suitable conditions. The point PK is constructed by applying the Tate p-adic uniformization of E to an ex...

Learning in a multiagent environment is complicated by the fact that as other agents learn, the environment eeectively changes. Moreover, other agents' actions are often not directly observable , and the actions taken by the learning agent can strongly bias which range of behaviors are encountered. We deene the concept of a conjectural equilibrium, where all agents' expectations are realized, a...

Learning in a multiagent environment is com plicated by the fact that as other agents learn the environment e ectively changes Moreover other agents actions are often not directly ob servable and the actions taken by the learning agent can strongly bias which range of behav iors are encountered We de ne the concept of a conjectural equilibrium where all agents expec tations are realized and eac...

For a variety over a local field, Bloch proposed a conjectural formula for the alternating sum of Artin conductor of `adic cohomology. We prove that the formula is valid modulo 2 if the variety has even dimension.

Learning in a multiagent environment is complicated by the fact that as other agents learn, the environment effectively changes. Moreover, other agents’ actions are often not directly observable, and the actions taken by the learning agent can strongly bias which range of behaviors are encountered. We define the concept of a conjectural equilibrium, where all agents’ expectations m-e realized, ...

We give an explicit conjectural formula for the motivic Euler characteristic of an arbitrary symplectic local system on the moduli space A3 of principally polarized abelian threefolds. The main term of the formula is a conjectural motive of Siegel modular forms of a certain type; the remaining terms admit a surprisingly simple description in terms of the motivic Euler characteristics for lower ...

Let k be a number field, f(x) ∈ k[x] a polynomial over k with f(0) 6= 0, and O∗ k,S the group of S-units of k, where S is an appropriate finite set of places of k. In this note, we prove that outside of some natural exceptional set T ⊂ O∗ k,S , the prime ideals of Ok dividing f(u), u ∈ O∗ k,S \ T , mostly have degree one over Q; that is, the corresponding residue fields have degree one over the...

Schur superpolynomials have been introduced recently as limiting cases of the Macdonald superpolynomials. It turns out that there are two natural super-extensions of the Schur polynomials: in the limit q = t = 0 and q = t→∞, corresponding respectively to the Schur superpolynomials and their dual. However, a direct definition is missing. Here, we present a conjectural combinatorial definition fo...

Humans and intelligent computer programs must often jump to the conclusion that the objects they can determine to have certain properties or relations are the only objects that do. Circumscription formalizes such conjectural reasoning.