Zobrazeno 1 - 10
of 71
pro vyhledávání: '"Borger, James A."'
Autor:
Borger, James, Jun, Jaiung
We set up some basic module theory over semirings, with particular attention to scheme theory over semirings. We show that while not all the usual definitions of vector bundle agree over semirings, all the usual definitions of line bundle do agree. W
Externí odkaz:
http://arxiv.org/abs/2405.18645
Autor:
Borger, James, Gurney, Lance
We extend the Serre-Tate theory of canonical lifts of ordinary abelian varieties to arbitrary unpolarised families of ordinary abelian varieties parameterised by a $p$-adic formal scheme $S$. We show that the canonical lift is the unique lift to $W(S
Externí odkaz:
http://arxiv.org/abs/1905.10495
Autor:
Borger, James, de Smit, Bart
We consider generalized $\Lambda$-structures on algebras and schemes over the ring of integers $\mathit{O}_K$ of a number field $K$. When $K=\mathbb{Q}$, these agree with the $\lambda$-ring structures of algebraic K-theory. We then study reduced fini
Externí odkaz:
http://arxiv.org/abs/1809.02295
Autor:
Borger, James, Saha, Arnab
Using Buium's theory of arithmetic differential characters, we construct a filtered $F$-isocrystal ${\bf H}(A)_K$ associated to an abelian scheme $A$ over a $p$-adically complete discrete valuation ring with perfect residue field. As a filtered vecto
Externí odkaz:
http://arxiv.org/abs/1712.09346
Autor:
Borger, James, Saha, Arnab
In this article, given a scheme $X$ we show the existence of canonical lifts of Frobenius maps in an inverse system of schemes obtained from the fiber product of the canonical prolongation sequence of arithmetic jet spaces $J^*X$ and a prolongation s
Externí odkaz:
http://arxiv.org/abs/1703.07010
Autor:
Borger, James, Saha, Arnab
Publikováno v:
Alg. Number Th. 13 (2019) 797-837
We introduce differential characters of Drinfeld modules. These are function-field analogues of Buium's p-adic differential characters of elliptic curves and of Manin's differential characters of elliptic curves in differential algebra, both of which
Externí odkaz:
http://arxiv.org/abs/1703.05677
Autor:
Borger, James, Gurney, Lance
Publikováno v:
Nagoya Math. J. 233 (2019) 193-213
We show that the canonical-lift construction for ordinary elliptic curves over perfect fields of characteristic $p>0$ extends uniquely to arbitrary families of ordinary elliptic curves, even over $p$-adic formal schemes. In particular, the universal
Externí odkaz:
http://arxiv.org/abs/1608.05912
Autor:
Borger, James, Grinberg, Darij
Publikováno v:
Selecta Mathematica, April 2016, Volume 22, Issue 2, pp 595--629
A subtraction-free definition of the big Witt vector construction was recently given by the first author. This allows one to define the big Witt vectors of any semiring. Here we give an explicit combinatorial description of the big Witt vectors of th
Externí odkaz:
http://arxiv.org/abs/1311.5031
Autor:
Borger, James M.
We extend the big and $p$-typical Witt vector functors from commutative rings to commutative semirings. In the case of the big Witt vectors, this is a repackaging of some standard facts about monomial and Schur positivity in the combinatorics of symm
Externí odkaz:
http://arxiv.org/abs/1310.3013
Autor:
Borger, James, Saha, Arnab
Publikováno v:
In Advances in Mathematics 31 July 2019 351:388-428
