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ROOT NUMBERS AND RANKS IN POSITIVE CHARACTERISTIC     POSITIVE CHARACTERISTIC  ROOT NUMBERS       font style='font-size:12px;'> 2015/7/6
Inspired by this, for the rational function field K = κ(u) over any finite field κ with characteristic 6= 2, we construct an explicit 2-parameter family Ec,d of non-isotrivial elli...
We discuss two elementary constructions for covers with fixed ramification in positive characteristic. As an application, we compute the number of certain classes of covers between projective lines br...
Abstract: We study the $k[G]$-module structure of the space of holomorphic differentials of a curve defined over an algebraically closed field of positive characteristic, for a cyclic group $G$ of ord...
Abstract: We introduce a family of L-series specialising to both L-series associated to certain Dirichlet characters over F_q[T] and to integral values of Carlitz-Goss zeta function associated to F_q[...
Abstract: In this paper, we prove that every iterative differential embedding problem over an algebraic function field in positive characteristic with an algebraically closed field of constants has a ...
Abstract: We study rational Cherednik algebras over an algebraically closed field of positive characteristic. We first prove several general results about category O, and then focus on rational Chered...
Let p be a prime integer, 1 ≤ s r integers, F a field of characteristic p.
Pre-Lie algebras in positive characteristic     Pre-Lie algebras  positive characteristic       font style='font-size:12px;'> 2010/11/23
In prime characteristic we introduce the notion of restricted pre-Lie algebra. We prove in the pre-Lie context the analogue to Jacobson's theorem for restricted Lie algebras. In particular, we prove t...
Let $C$ be a smooth plane curve of degree $d$. A point $P$ in the projective plane is said to be Galois with respect to $C$ if the function field extension induced from the point projection from $P$ ...
We prove the $p$-parity conjecture for elliptic curves over global fields of characteristic $p > 3$. We also present partial results on the $\ell$-parity conjecture for primes $\ell \neq p$.
We offer a groupoid-theoretic approach to computing invariants. We illustrate this approach by describing the Gel'fand-MacPherson correspondence and the Gale transform as well as giving Zariski-local...
If C  P3 k is an integral curve and k an algebraically closed field of characteristic 0, it is known that the points of the general plane section C \H of C are in uniform position. From this it follo...
Laudal's Lemma in positive characteristic      Laudal's Lemma  positive characteristic        font style='font-size:12px;'> 2010/12/9
Laudal’s Lemma states that if C is a curve of degree d > s2 + 1 in P3 over an algebraically closed field of characteristic 0 such that its plane section is contained in an irreducible curve of degree ...
There have been a number of recent papers on the representation growth of various families of groups. In particular, see [LL], where very good estimates were given for the zeta function counting the c...
This paper can be looked as a continues work of [3] where the authors classified all the Hopf structures on monomial coalgebras over a field of characteristic zero and containing all roots of unity. L...

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