On topological and combinatorial structures of pointed stable curves over algebraically closed fields of positive characteristic
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DOI: 10.1002/mana.202100053
Abstract: In the present paper, we study anabelian geometry of curves over algebraically closed fields of positive characteristic. Let X• = (X,DX) be a pointed stable curve over an algebraically closed field of characteristic p >… read more here.
Keywords: closed fields; positive characteristic; pointed stable; fields positive ... See more keywords
On the Arakelov inequality in positive characteristic
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DOI: 10.1007/s00209-017-1945-5
Abstract: In this note, we generalize the Arakelov inequality in positive characteristic for non-isotrivial semistable families of curves of $$g\ge 2$$g≥2 which are liftable to $$W_2(k)$$W2(k) (resp. W(k)). As a consequence, we give an analogue of… read more here.
Keywords: positive characteristic; arakelov inequality; inequality positive;
Nonuniform Discrete Wavelets on Local Fields of Positive Characteristic
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DOI: 10.1007/s11785-018-0813-6
Abstract: A constructive algorithm based on the theory of spectral pairs for constructing nonuniform wavelet basis in $$L^2(\mathbb R)$$L2(R) was considered by Gabardo and Nashed (J Funct Anal 158:209–241, 1998). In this setting, the associated translation… read more here.
Keywords: nonuniform discrete; discrete wavelets; positive characteristic; wavelets local ... See more keywords
Some hypergeometric functions in positive characteristic and transcendence
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DOI: 10.1016/j.crma.2019.03.006
Abstract: Abstract In this work, we study some special hypergeometric functions in positive characteristic, introduced by D. S. Thakur. We shall establish functional relationships among them, and deduce, with the help of the function field version… read more here.
Keywords: hypergeometric functions; functions positive; characteristic transcendence; positive characteristic ... See more keywords
Minimal extensions of Tannakian categories in positive characteristic
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DOI: 10.1016/j.jalgebra.2022.03.025
Abstract: . We extend [DGNO1, Theorem 4.5] and [LKW, Theorem 4.22] to positive characteristic (i.e., to the finite, not necessarily fusion, case). Namely, we prove that if D is a finite nondegenerate braided tensor category over… read more here.
Keywords: minimal extensions; ext rep; extensions tannakian; rep ... See more keywords
Exponential matrices
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DOI: 10.1016/j.laa.2019.02.024
Abstract: In this article, we introduce a notion of an exponential matrix, which is a polynomial matrix with exponential properties, and a notion of an equivalence relation of two exponential matrices, and then we initiate to… read more here.
Keywords: equivalence; positive characteristic; exponential matrices; characteristic equivalence ... See more keywords
Topology of moduli spaces of curves and anabelian geometry in positive characteristic
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DOI: 10.1017/fms.2024.12
Abstract: Abstract In the present paper, we study a new kind of anabelian phenomenon concerning the smooth pointed stable curves in positive characteristic. It shows that the topology of moduli spaces of curves can be understood… read more here.
Keywords: moduli spaces; spaces curves; topology moduli; positive characteristic ... See more keywords
A SPARSITY RESULT FOR THE DYNAMICAL MORDELL–LANG CONJECTURE IN POSITIVE CHARACTERISTIC
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DOI: 10.1017/s0004972721000083
Abstract: Abstract We prove a quantitative partial result in support of the dynamical Mordell–Lang conjecture (also known as the DML conjecture) in positive characteristic. More precisely, we show the following: given a field K of characteristic… read more here.
Keywords: lang conjecture; mordell lang; dynamical mordell; conjecture positive ... See more keywords
Model theory of fields with free operators in positive characteristic
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DOI: 10.1090/tran/7896
Abstract: We give algebraic conditions for a finite commutative algebra B B over a field of positive characteristic, which are equivalent to the companionability of the theory of fields with “ B B -operators” (i.e., the… read more here.
Keywords: model theory; theory fields; fields free; positive characteristic ... See more keywords
Bernstein-Sato theory for arbitrary ideals in positive characteristic
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DOI: 10.1090/tran/8271
Abstract: Mustaţă defined Bernstein-Sato polynomials in prime characteristic for principal ideals and proved that the roots of these polynomials are related to the F F -jumping numbers of the ideal. This approach was later refined by… read more here.
Keywords: ideals positive; positive characteristic; theory arbitrary; sato theory ... See more keywords
Cohomological Invariants in Positive Characteristic
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DOI: 10.1093/imrn/rnaa321
Abstract: We determine the mod $p$ cohomological invariants for several affine group schemes $G$ in characteristic $p$. These are invariants of $G$-torsors with values in étale motivic cohomology, or equivalently in Kato’s version of Galois cohomology… read more here.
Keywords: positive characteristic; cohomology; invariants positive; cohomological invariants ... See more keywords